{"id":27236,"date":"2023-04-03T21:27:15","date_gmt":"2023-04-03T21:27:15","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27236"},"modified":"2024-02-05T16:07:55","modified_gmt":"2024-02-05T16:07:55","slug":"diagonal-of-a-rectangle-properties-formula-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle","title":{"rendered":"Diagonal of a Rectangle &#8211; Properties, Formula, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-f7b851b0-adbc-4376-9292-b6aa00b5d24d\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#0-what-are-diagonals-of-a-rectangle>What Are Diagonals of a Rectangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#2-properties-of-diagonals-of-a-rectangle>Properties of Diagonals of a Rectangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#4-diagonal-of-a-rectangle-formula-derivation>Diagonal of a Rectangle Formula Derivation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#8-solved-examples-for-diagonals-of-a-rectangle>Solved Examples for Diagonals of a Rectangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#9-practice-problems-on-diagonals-of-a-rectangle>Practice Problems on Diagonals of a Rectangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle#10-frequently-asked-questions-about-diagonals-of-a-rectangle>Frequently Asked Questions about Diagonals of a Rectangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-diagonals-of-a-rectangle\">What Are Diagonals of a Rectangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Diagonals of a rectangle are line segments connecting opposite vertices of a rectangle. <\/strong>A rectangle is a quadrilateral in which opposite sides are equal and all angles measure $90^\\circ$.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"311\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/length-width-and-four-angles-of-a-rectangle.png\" alt=\"length, width, and four angles of a rectangle\" class=\"wp-image-33748\" title=\"length, width, and four angles of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/length-width-and-four-angles-of-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/length-width-and-four-angles-of-a-rectangle-300x150.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A diagonal is a line segment connecting two non-adjacent vertices of a polygon. The word diagonal comes from the ancient Greek word \u201c<em>diagonios<\/em>,\u201d (Latin <em>diagonalis)<\/em><em> <\/em>which means \u201cfrom angle to angle.\u201d&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Both Euclid and Strabo used it to describe a line that connects two vertices of a cuboid or a rhombus; later, it became known in Latin as diagonus (slanting line).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle.png\" alt=\"Diagonal of a rectangle\" class=\"wp-image-33749\" title=\"Diagonal of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-diagonals-of-a-rectangle-definition\">Diagonals of a Rectangle Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>A line segment that connects any two opposite vertices of a rectangle is called diagonal of a rectangle.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider \u25adABCD. A rectangle with diagonals AC and BD as shown below.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,&nbsp; $AC = BD$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle-1.png\" alt=\"Rectangle with diagonals\" class=\"wp-image-33750\" title=\"Rectangle with diagonals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/diagonal-of-a-rectangle-1-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-circles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_circles_rectangles_pt.png\" alt=\"Identify Circles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Circles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-kite-squares-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_square_rectangle_pt.png\" alt=\"Identify Kite, Squares and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Kite, Squares and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-rectangles-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_3_6_gm.png\" alt=\"Match Rectangles and Circles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Rectangles and Circles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_1_pt.png\" alt=\"Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-properties-of-diagonals-of-a-rectangle\">Properties of Diagonals of a Rectangle<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"358\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/properties-of-diagonals.png\" alt=\"Properties of diagonals\" class=\"wp-image-33751\" title=\"Properties of diagonals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/properties-of-diagonals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/properties-of-diagonals-300x173.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonals of a rectangle are congruent.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">$\\left[AC = BD\\right]$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Each diagonal divides a rectangle into two congruent right-angled triangles.<\/li>\n<\/ol>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonals of a rectangle are <strong>not perpendicular<\/strong> to each other.<\/li>\n<\/ol>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If two diagonals of a rectangle bisect each other at $90^\\circ$, it is called a square.<\/li>\n<\/ol>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When two diagonals intersect, they form one obtuse angle and one acute angle. The opposite central angles are equal.<\/li>\n<\/ol>\n\n\n\n<ol start=\"6\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Adjacent angles formed by the diagonals are supplementary.<\/li>\n<\/ol>\n\n\n\n<ol start=\"7\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Diagonals of a rectangle form the hypotenuse of the right triangle.<\/li>\n<\/ol>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-diagonal-of-a-rectangle-formula\">Diagonal of a Rectangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal of a rectangle formula helps in finding the length of the diagonal when the length and width of the rectangle are known.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A diagonal divides a rectangle into two right triangles, each of which has a hypotenuse and sides that are equal to the sides of the rectangle. The diagonal is that hypotenuse.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"453\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-diagonal-of-rectangle.png\" alt=\"Formula for diagonal of rectangle\" class=\"wp-image-33752\" title=\"Formula for diagonal of rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-diagonal-of-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-diagonal-of-rectangle-300x219.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">So, how to find the diagonal of a rectangle? What is the diagonal measurement of a rectangle?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal length of a rectangle is calculated using the formula, $d = \\sqrt{(w^2 + l^2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where, $d = diagonal$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$l&nbsp; = length$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$w&nbsp; = width$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This formula can be used to find the measurement of the length of a diagonal of a rectangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-diagonal-of-a-rectangle-formula-derivation\">Diagonal of a Rectangle Formula Derivation<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal of a rectangle formula is derived using the Pythagoras\u2019 Theorem. Split the rectangle into two right triangles formed by a diagonal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/derivation-of-the-diagonal-of-a-rectangle.png\" alt=\"Derivation of the diagonal of a rectangle\" class=\"wp-image-33753\" title=\"Derivation of the diagonal of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/derivation-of-the-diagonal-of-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/derivation-of-the-diagonal-of-a-rectangle-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Applying Pythagoras\u2019 Theorem in the right triangle PSR, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d^2 = b^2 + l^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,&nbsp; $d =$ diagonal, $l =$ length, $b =$ breadth<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Taking square root on both sides,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = \\sqrt{(b^2 + l^2)}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$l =$ length of the rectangle<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$b =$&nbsp; breadth of the rectangle<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Simply substitute the values of the length and breadth in the formula to get the answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"310\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/finding-the-length-of-the-diagonal-of-a-rectangle.png\" alt=\"Finding the length of the diagonal of a rectangle\" class=\"wp-image-33754\" title=\"Finding the length of the diagonal of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/finding-the-length-of-the-diagonal-of-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/finding-the-length-of-the-diagonal-of-a-rectangle-300x150.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above rectangle,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of diagonal $= d = \\sqrt{3^2 + 4^2} =&nbsp;\\sqrt{9 + 16} = \\sqrt{25} = 5$ units<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-angles-made-by-diagonals-of-a-rectangle\">Angles Made by Diagonals of a Rectangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">As discussed above, if the diagonals of the polygon bisect each other, it is called a square.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonals of a rectangle are equal in length, bisect each other. They do not meet at a right angle in the center. The diagonals of a rectangle do not bisect the interior angles of the rectangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>Take a look at the image given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"518\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-formed-by-diagonals-of-a-rectangle.png\" alt=\"Angles formed by diagonals of a rectangle\" class=\"wp-image-33755\" title=\"Angles formed by diagonals of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-formed-by-diagonals-of-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angles-formed-by-diagonals-of-a-rectangle-300x251.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the image given above, AC and BD are the diagonals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Angles formed by diagonal AC and BD are $\\angle AED,\\; \\angle AEB,\\; \\angle BEC$, and $\\angle DEC$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">These angles do not meet at right angles, but the adjacent angles are supplementary, which means the adjacent angle-pairs add up to $180^\\circ$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\angle AED + \\angle AEB = 180^\\circ$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle AEB + \\angle BEC = 180^\\circ$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle BEC + \\angle DEC = 180^\\circ$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle AED + \\angle DEC = 180^\\circ$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-facts-about-diagonals-of-a-rectangle\">Facts about Diagonals of a Rectangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The two diagonals of a rectangle divide the rectangle into four triangles.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Each diagonal of a rectangle divides it into two congruent right triangles.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The intersection of the diagonals is the circumcenter. That is, you can draw a circle with that at the center to pass through the four corners.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Thus, diagonal $= 2r$ \u2026where r is the radius of the circumcircle<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"368\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/intersection-of-diagonals-of-a-rectangle-forms-the-circumcenter.png\" alt=\"Intersection of diagonals of a rectangle forms the circumcenter\" class=\"wp-image-33756\" title=\"Intersection of diagonals of a rectangle forms the circumcenter\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/intersection-of-diagonals-of-a-rectangle-forms-the-circumcenter.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/intersection-of-diagonals-of-a-rectangle-forms-the-circumcenter-300x178.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">We can calculate the length of the diagonal of the rectangle using the formula:&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$d = \\sqrt{(b^2 + l^2)}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The rectangle is called a square if its diagonals bisect each other at right angles.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">As the diagonals are generally slanted, a slanted symbol \u201c \/ \u201d is used to denote diagonals.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we have learned about diagonals of the rectangle, its properties, formulas, and facts. Now let&#8217;s solve some examples based on the formulas learned above.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples-for-diagonals-of-a-rectangle\">Solved Examples for Diagonals of a Rectangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Identify the length, width and diagonal in the given rectangle.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"169\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangle-abcd.png\" alt=\"Rectangle ABCD\" class=\"wp-image-33757\" title=\"Rectangle ABCD\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length $\\rightarrow$ AD and BC<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Width $\\rightarrow$ AB and CD<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonals $\\rightarrow$ AC and BD<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the length of each diagonal of a rectangle of length 15 units and width 8 units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the rectangle, $l&nbsp; = 15$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Breadth of the rectangle, $b = 8$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the diagonal $= d = \\sqrt{(b^2 + l^2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d =&nbsp; \\sqrt{(8^2 + 15^2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d =&nbsp; \\sqrt{(64 + 225)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d = \\sqrt{289}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d = 17$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The length of the diagonal is 17 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. A rectangular park is 30 ft long and 16 ft wide. Determine the diagonal of the rectangular park.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the rectangular park $= 30$ ft&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Breadth of the rectangular park $= 15$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the diagonal $d = \\sqrt{(b^2 + l^2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= sqrt{(16^2 + 30^2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\sqrt{(256+ 900)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\sqrt{1156}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 34$ ft<br><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal of the rectangular park is 34 ft.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Find the length of the diagonal of the given rectangle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"182\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/a-rectangle-with-length-12-in-and-width-5-in.webp\" alt=\"A rectangle with length 12 in and width 5 in\" class=\"wp-image-33758\" title=\"A rectangle with length 12 in and width 5 in\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length $= 12$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Breadth $= 5$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonal $= ?$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Using the Pythagorean theorem, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$l^2 + b^2&nbsp; = d^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$12^2 + 5^2 = d^2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$d^2 = 144 + 25$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$d^2 = 169$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Taking the square root&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = 13$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Find the length of the rectangle if the breadth of the rectangle is 3 inches, and the diagonal of the rectangle is 5 inches.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Breadth of the rectangle $= 3$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonal of the rectangle (hypotenuse) $= 5$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here we will apply Pythagoras\u2019 Theorem.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(Hypotenuse)^2 = (Length)^2 + (Breadth)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$5^2 = &nbsp;l^2 + 3^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$l^2 = 5^2 \\;-\\; 3^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$l^2 = 25 \\;-\\; 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$l&nbsp; = \\sqrt{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$l&nbsp; =&nbsp; 4$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;Length of the rectangle is 4 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems-on-diagonals-of-a-rectangle\">Practice Problems on Diagonals of a Rectangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Diagonal of a Rectangle - Properties, Formula, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">A line segment that connects any two opposite vertices of a rectangle is said to be its _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">diagonal<\/div><div class=\"spq_answer_block\" data-value=\"1\">length<\/div><div class=\"spq_answer_block\" data-value=\"2\">breadth<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: diagonal<br\/>A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The diagonals of a rectangle are ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">perpendicular<\/div><div class=\"spq_answer_block\" data-value=\"1\">equal<\/div><div class=\"spq_answer_block\" data-value=\"2\">not equal<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: equal<br\/>The diagonals of a rectangle are equal in length.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is NOT TRUE ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Each diagonal divides a rectangle into 2 congruent right triangles.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Diagonals of a rectangle bisect each other.<\/div><div class=\"spq_answer_block\" data-value=\"2\">The length of the diagonals of a rectangle is equal.<\/div><div class=\"spq_answer_block\" data-value=\"3\">The diagonals of a rectangle are perpendicular to each other.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: The diagonals of a rectangle are perpendicular to each other.<br\/>The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $90^\\circ$, it is called a square.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The length of diagonals of the rectangle is calculated using formula _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$d = \\sqrt{2(b^2 + l^2)}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$d = \\sqrt{(b^2\\;-\\;l^2)}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$d = \\sqrt{(b^2+l^2)}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$d = \\sqrt{(b^2 +2\\;l^2)}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $d = \\sqrt{(b^2+l^2)}$<br\/>The length of diagonals of the rectangle is calculated using formula: $d = \\sqrt{(b^2 + l^2)}$<br>\r\nwhere, $d =$ diagonal of rectangle<br>\r\n             $l =$ length of the rectangle<br>\r\n            $b =$ breadth of the rectangle<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Adjacent angles formed by the diagonals of a rectangle are ________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">supplementary<\/div><div class=\"spq_answer_block\" data-value=\"1\">congruent<\/div><div class=\"spq_answer_block\" data-value=\"2\">complementary<\/div><div class=\"spq_answer_block\" data-value=\"3\">straight<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: supplementary<br\/>Adjacent angles formed by the diagonals are supplementary.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Diagonal of a Rectangle - Properties, Formula, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Diagonal of a Rectangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    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\"Comment\",\n                                    \"text\": \"A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"breadth\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"diagonal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A line segment that connects any two opposite vertices of a rectangle is said to be its diagonal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The diagonals of a rectangle are ______.\",\n                    \"text\": \"The diagonals of a rectangle are ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The diagonals of a rectangle are equal in length.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are equal in length.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"not equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are equal in length.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are equal in length.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"equal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The diagonals of a rectangle are equal in length.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The diagonals of a rectangle are equal in length.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is NOT TRUE ?\",\n                    \"text\": \"Which of the following is NOT TRUE ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Each diagonal divides a rectangle into 2 congruent right triangles.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Diagonals of a rectangle bisect each other.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The length of the diagonals of a rectangle is equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The diagonals of a rectangle are perpendicular to each other.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The diagonals of a rectangle are not perpendicular to each other. When two diagonals bisect each other at $$90^\\\\circ$$, it is called a square.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The length of diagonals of the rectangle is calculated using formula _________.\",\n                    \"text\": \"The length of diagonals of the rectangle is calculated using formula _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = \\\\sqrt{2(b^2 + l^2)}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = \\\\sqrt{(b^2\\\\;-\\\\;l^2)}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$d = \\\\sqrt{(b^2 +2\\\\;l^2)}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$d = \\\\sqrt{(b^2+l^2)}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The length of diagonals of the rectangle is calculated using formula: $$d = \\\\sqrt{(b^2 + l^2)}$$<br>\r\nwhere, $$d =$$ diagonal of rectangle<br>\r\n             $$l =$$ length of the rectangle<br>\r\n            $$b =$$ breadth of the rectangle\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Adjacent angles formed by the diagonals of a rectangle are ________.\",\n                    \"text\": \"Adjacent angles formed by the diagonals of a rectangle are ________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"congruent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"complementary\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"straight\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"supplementary\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Adjacent angles formed by the diagonals are supplementary.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions-about-diagonals-of-a-rectangle\">Frequently Asked Questions about Diagonals of a Rectangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>Why are the diagonals of a rectangle equal in length?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">A rectangle is a quadrilateral where all the angles are right angles. A rectangle is also a parallelogram where the opposite sides are equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider this rectangle ABCD.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"169\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangle-abcd-1.png\" alt=\"A rectangle ABCD\" class=\"wp-image-33759\" title=\"A rectangle ABCD\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above rectangle, consider triangles ABC and DCB.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\angle ABC = \\angle DCB = 90$&nbsp; [Angles of rectangle]<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$BC = BC$ (common side)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$AB&nbsp; = DC$ (Opposite sides of a parallelogram are equal)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $ABC\\congDCB$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$AC = DB$ [CPCTC]<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the diagonals of a rectangle are equal.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>Do diagonals of a rectangle always bisect each other?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">The diagonals of a rectangle always bisect each other. However, they do not meet at 90 degrees except if the rectangle is a square.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>What is the formula for the area of a rectangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">Area of a rectangle is given by the product of length and breadth.Area of rectangle $= l\\timesb$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>Why is the area of the rectangle the product of length and breadth?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">Let us understand why the area of the rectangle is $length \\times breadth$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider \u25ad ABCD. We can see that the diagonal AC divides the rectangle into two congruent triangles, $\\Delta ABC$ and $\\Delta ADC$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"181\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/aiagonal-ac-of-a-rectangle-abcd.webp\" alt=\"Diagonal AC of a rectangle ABCD\" class=\"wp-image-33761\" title=\"Diagonal AC of a rectangle ABCD\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Area of Rectangle $ABCD =$ Area of Triangle $ABC +$ Area of Triangle ADC<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 2\\times$ Area of Triangle ABC<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 2 \\times (\\frac{1}{2} \\times Base \\times Height)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= AB \\times BC$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= Length \\times Breadth$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the rectangle is the product of length and breadth.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>How many diagonals are there in a rectangle?<\/strong> <strong>Are the diagonals of a rectangle always congruent?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">A rectangle has two diagonals. Each diagonal divides a rectangle into two right triangles. The two diagonals of a rectangle are always congruent.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\"><strong>Are diagonals perpendicular in a rectangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-b53b8f4a-fcd3-4e17-98f2-e1e8d0c2f199\">\n\n<p class=\"eplus-wrapper\">No! The two diagonals of a rectangle do not intersect at right angles.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Diagonals of a Rectangle? Diagonals of a rectangle are line segments connecting opposite vertices of a rectangle. A rectangle is a quadrilateral in which opposite sides are equal and all angles measure $90^\\circ$.&nbsp; A diagonal is a line segment connecting two non-adjacent vertices of a polygon. The word diagonal comes from the ancient &#8230; <a title=\"Diagonal of a Rectangle &#8211; Properties, Formula, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonals-of-rectangle\" aria-label=\"More on Diagonal of a Rectangle &#8211; Properties, Formula, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27236","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27236","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27236"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27236\/revisions"}],"predecessor-version":[{"id":39956,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27236\/revisions\/39956"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}