{"id":25413,"date":"2023-02-23T18:08:13","date_gmt":"2023-02-23T18:08:13","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25413"},"modified":"2024-01-16T10:07:56","modified_gmt":"2024-01-16T10:07:56","slug":"hypotenuse-in-right-triangle","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse","title":{"rendered":"Hypotenuse in Right Triangle &#8211; Definition, Formula"},"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-a4d24942-69d8-4f63-932b-6adcf5a18434\" 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\/hypotenuse#0-what-is-a-hypotenuse>What Is a Hypotenuse?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse#2-theorem-for-the-hypotenuse>Theorem for the Hypotenuse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse#4-formula-of-the-hypotenuse>Formula of the Hypotenuse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse#9-solved-examples-on-hypotenuse>Solved Examples on Hypotenuse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse#10-practice-problems-on-hypotenuse>Practice Problems on Hypotenuse<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse#11-frequently-asked-questions-on-hypotenuse>Frequently Asked Questions on Hypotenuse<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-hypotenuse\">What Is a Hypotenuse?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>A right-angled triangle is a triangle that has one interior angle, which measures 90 degrees. The side opposite to the right angle in a right-angled triangle is known as the hypotenuse. It is the longest side.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"517\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/hypotenuse-is-the-longest-side-of-a-right-triangle.png\" alt=\"Hypotenuse is the longest side of a right triangle\" class=\"wp-image-36795\" title=\"Hypotenuse is the longest side of a right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/hypotenuse-is-the-longest-side-of-a-right-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/hypotenuse-is-the-longest-side-of-a-right-triangle-300x250.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-hypotenuse\">Definition of Hypotenuse?<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The sides of a right triangle are base, perpendicular, and hypotenuse. As mentioned earlier, the hypotenuse of a right triangle lies opposite to the right angle. In a right-angled triangle, the sides other than the hypotenuse which determine the right angle are also referred to as \u201clegs.\u201d The side that makes a right angle with the base is called the perpendicular.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the definition of the hypotenuse in geometry can be given as the longest side in a right triangle that lies opposite to the right angle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"490\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/base-height-and-hypotenuse.png\" alt=\"Base, height and hypotenuse\" class=\"wp-image-36797\" title=\"Base, height and hypotenuse\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/base-height-and-hypotenuse.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/base-height-and-hypotenuse-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-theorem-for-the-hypotenuse\">Theorem for the Hypotenuse<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The famous Pythagoras\u2019 theorem defines the <strong>hypotenuse<\/strong> theorem. As per this theorem, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides of the triangle, i.e., the base and perpendicular side.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Base\u00b2 <\/strong>$+$<strong> Perpendicular\u00b2 <\/strong>$=$<strong> Hypotenuse<sup>2<\/sup><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-proof-of-the-hypotenuse-theorem\">Proof of the Hypotenuse Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Do you wonder how the <strong>hypotenuse<\/strong> theorem was derived? Let\u2019s understand its proof.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"590\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/right-angled-triangle-ABC.png\" alt=\"Right-angled triangle ABC\" class=\"wp-image-36798\" title=\"Right-angled triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/right-angled-triangle-ABC.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/right-angled-triangle-ABC-300x285.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The triangle ABC is a right-angled triangle such that m$\\angle$B $= 90^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB is the base side, BC is the perpendicular side, and AC is the hypotenuse side.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We need to prove that AB\u00b2 $+$ BC\u00b2 $=$ AC\u00b2<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For this, we draw a line from B to meet the side AC at point D.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"481\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-hypotenuse-theorem.png\" alt=\"Proof of hypotenuse theorem\" class=\"wp-image-36799\" title=\"Proof of hypotenuse theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-hypotenuse-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-hypotenuse-theorem-300x233.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Using the similar triangle theorem, we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Delta$ADB ~ $\\Delta$ABC&nbsp; by AAA similarity<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, its corresponding sides are proportional.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{AD}{AB} = \\frac{AB}{AC}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB\u00b2 $=$ AD $\\times$ AC&nbsp; &#8211; (i)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, using the similar triangle theorem again, we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Delta$BDC ~ $\\Delta$ABC<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\frac{AD}{AB} = \\frac{AB}{AC}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">That is BC\u00b2 $=$ CD $\\times$AC &#8211; (ii)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, by adding (i) and (ii), we will get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB\u00b2 $+$ BC\u00b2 $=$ (AD $\\times$ AC) + (CD $\\times$ AC)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB\u00b2 $+$ BC\u00b2 $=$ AC (AD $+$ CD)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB\u00b2 $+$ BC\u00b2 $=$ AC (AC)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AB\u00b2 $+$ BC\u00b2 $=$ AC\u00b2<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC\u00b2 $=$ AB\u00b2 $+$ BC\u00b2&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can also write this as<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Hypotenuse\u00b2 <\/strong>$=$<strong> Base\u00b2 <\/strong>$+$<strong> Perpendicular\u00b2<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-formula-of-the-hypotenuse\">Formula of the Hypotenuse<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">How to find the hypotenuse of a right triangle? We can use the formula that includes the length of the base and the perpendicular.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The <strong>formula for a hypotenuse<\/strong> is<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Hypotenuse <\/strong>$= \\sqrt{Base\u00b2 + Perpendicular\u00b2}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"532\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-for-hypotenuse.png\" alt=\"Formula for hypotenuse\" class=\"wp-image-36800\" title=\"Formula for hypotenuse\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-for-hypotenuse.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-for-hypotenuse-300x257.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In a right-angled triangle ABC,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hypotenuse $= c$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Base $= b$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perpendicular or Altitude $= a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;<\/strong>$a^{2} + b^{2} = c^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>How to Calculate the Length of the Hypotenuse of a Right Triangle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand the steps for the <strong>calculation of the length of the hypotenuse of a right triangle<\/strong> when base and height are given.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"551\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-hypotenuse.png\" alt=\"Finding the length of hypotenuse\" class=\"wp-image-36801\" title=\"Finding the length of hypotenuse\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-hypotenuse.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-hypotenuse-300x266.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We know that the base side, i.e., AB $= 4$ inches, and the perpendicular side, i.e., BC $= 3$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To find the length of the <strong>hypotenuse, <\/strong>we need to use the above formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Hypotenuse <\/strong>$=$<strong> Base\u00b2 <\/strong>$+$<strong> Perpendicular\u00b2<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC $= \\sqrt{(AB)\u00b2 + (BC)\u00b2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC $= \\sqrt{(4)\u00b2 + (3)\u00b2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC $= \\sqrt{16 + 9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC $= \\sqrt{25}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">AC $= 5$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the <strong>hypotenuse<\/strong> of the right triangle ABC is 5 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-find-the-altitude-drawn-on-a-hypotenuse\">How To Find the Altitude Drawn on a Hypotenuse?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The altitude on a <strong>hypotenuse<\/strong> is the perpendicular drawn on the hypotenuse that connects a right triangle\u2019s hypotenuse to its opposite vertex.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"555\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-drawn-on-a-hypotenuse.png\" alt=\"Altitude drawn on a hypotenuse\" class=\"wp-image-36802\" title=\"Altitude drawn on a hypotenuse\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-drawn-on-a-hypotenuse.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/altitude-drawn-on-a-hypotenuse-300x269.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">To find the altitude on a hypotenuse, let\u2019s take an example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"555\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-the-altitude-of-right-triangle.png\" alt=\"Finding the length of the altitude of right triangle\" class=\"wp-image-36803\" title=\"Finding the length of the altitude of right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-the-altitude-of-right-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-length-of-the-altitude-of-right-triangle-300x269.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">From the right-angled triangle ABC, we know that,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Base $= 6$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perpendicular $= 8$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hypotenuse $= 10$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To find the altitude, we divide the shortest side by the hypotenuse of $\\Delta$ABC, i.e., Base\/Hypotenuse $= \\frac{6}{10} = \\frac{3}{5}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Finally, we multiply this value by the value of the remaining side of the $\\Delta$ABC, i.e.,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{5} \\times $ perpendicular $= \\frac{3}{5} \\times 8 = \\frac{24}{5} = 4.8$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the value of the altitude in $\\Delta$ABC is 4.8 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-area-of-an-isosceles-right-triangle\">Area of an Isosceles Right Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Generally, the area of an isosceles right triangle is calculated with the help of this simple formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area <\/strong>$= \\frac{1}{2}$<strong> Base <\/strong>$\\times$<strong> Perpendicular (or altitude)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since an isosceles right triangle has two equal sides, we can also write the formula as:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area <\/strong>$= \\frac{1}{2}\\times$<strong> (Base)\u00b2<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area <\/strong>$= \\frac{1}{2}\\times$<strong> (Perpendicular)\u00b2.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example: Calculate the area of the isosceles right triangle given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"440\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/Isosceles-right-triangle.png\" alt=\"Isosceles right triangle\" class=\"wp-image-36804\" title=\"Isosceles right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/Isosceles-right-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/Isosceles-right-triangle-300x213.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We know that the base side, i.e., DE $= 9$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the area of the isosceles right triangle $= \\frac{1}{2}\\times$ (Base)\u00b2<\/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; $=\\frac{1}{2}\\times$ (DE)\u00b2<\/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;$= \\frac{1}{2}\\times (9)\u00b2$<\/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; $= \\frac{1}{2}\\times 81$<\/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; $= 40.5$ inches\u00b2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In scenarios where only the <strong>hypotenuse<\/strong> of an isosceles right triangle is given, we can still find its area. Let\u2019s understand this better with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: Find the area of the isosceles right triangle whose hypotenuse is 12 feet.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that hypotenuse $= \\sqrt{(base\u00b2 + perpendicular\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the triangle is isosceles, hypotenuse $= \\sqrt{(base\u00b2 + base\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$12 = \\sqrt{2(base)^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(12)\u00b2 = 2(base\u00b2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the squares on either side will cancel each other out, and we will get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$12 = 2(base)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{12}{2} \\times = base$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$6 = base$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the base $= 6$ feet $=$ perpendicular.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, since we know the sides of an isosceles triangle other than its hypotenuse, we can find its area by using the formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{1}{2} \\times (Base)\u00b2 = \\frac{1}{2} \\times (6)\u00b2 = \\frac{1}{2} \\times 36 = 18$ inches\u00b2.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-fun-facts\">Fun Facts<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Did you know that the word <strong>hypotenuse<\/strong> is derived from the Greek word <em>hypoteinousa<\/em>? \u201cHypoteinousa\u201d means \u201cstretching under (a right angle).\u201d<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The relationship between altitude on a hypotenuse and a right-angled triangle is explained by the Right Triangle Altitude Theorem. As per this theorem, altitude on the hypotenuse of a right-angled triangle divides it into two congruent right-angled triangles. The two triangles are similar to the main right-angled triangle.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In a right-angled triangle, the altitude on the hypotenuse can also be calculated with the help of basic trigonometric ratios.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, the <strong>hypotenuse<\/strong> is defined as the side opposite the right angle in a right-angled triangle. Its theorem is defined by Pythagoras\u2019 theorem (Hypotenuse\u00b2 $=$ Base\u00b2 $+$ Perpendicular\u00b2). This formula helps us find the hypotenuse and area of a right triangle or an isosceles right triangle in math and for real-life objects as well.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-hypotenuse\">Solved Examples on Hypotenuse<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the length of the hypotenuse DF.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-length-of-hypotenuse.png\" alt=\"Finding length of hypotenuse\" class=\"wp-image-36805\" title=\"Finding length of hypotenuse\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-length-of-hypotenuse.png 416w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-length-of-hypotenuse-300x270.png 300w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the base side (EF) $= 5$ inches and the perpendicular (DE) $= 12$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hypotenuse $= \\sqrt{(base\u00b2 + perpendicular\u00b2)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;   $= \\sqrt{\\left\\{(5)\u00b2 + (12)\u00b2\\right\\}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;   $= \\sqrt{25+144}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;   $= \\sqrt{169}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;               $= 13$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the length of the hypotenuse (DF) is 13 inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Hypotenuse <\/strong>$= 100$<strong> feet, Base <\/strong>$= 8$<strong> feet. Find the height of the right triangle.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hypotenuse\u00b2 $=$ Base\u00b2 $+ $Perpendicular\u00b2.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100 = 8^{2} +$ Perpendicular\u00b2<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perpendicular\u00b2 $= 100 \\;-\\;64$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perpendicular\u00b2 $= 36$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perpendicular $= 6$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the area of a right triangle whose base and perpendicular are 10 feet each.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">When the triangle is isosceles (base side = perpendicular side), the formula finding the area<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{2} \\times$(perpendicular)\u00b2<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{2} \\times (10)\u00b2&nbsp;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{1}{2} \\times 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 50$ feet\u00b2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Find the base of the right-angled sandwich.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-side-of-right-triangle.png\" alt=\"Finding the missing side of right triangle\" class=\"wp-image-36806\" title=\"Finding the missing side of right triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-side-of-right-triangle.png 507w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-side-of-right-triangle-300x221.png 300w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We know that hypotenuse $= 17$ inches and perpendicular $= 15$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since hypotenuse\u00b2 $=$ (base\u00b2 $+$ perpendicular\u00b2).<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, base\u00b2 $=$ (hypotenuse\u00b2 $-$ perpendicular\u00b2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">base\u00b2 $= (17)\u00b2 \\;-\\; (15)\u00b2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">base\u00b2 $= 289 \\;-\\; 225$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">base\u00b2 $= 64$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">base\u00b2 $= (8)\u00b2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Squares on each side will cancel each other, and we will get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Base $= 8$ inches.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Determine the altitude of a right triangle whose hypotenuse, base, and perpendicular are 15, 9, and 12 inches.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>To find the altitude, we need to divide the shortest side (here, base) by the hypotenuse.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Base\/Hypotenuse $= \\frac{9}{15} = \\frac{3}{5}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, we need to multiply the above value by the remaining side, i.e., the perpendicular side.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{5} \\times$ perpendicular $= \\frac{3}{5} \\times 12 = \\frac{36}{5} = 7.2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the altitude of the right triangle is 7.2 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-hypotenuse\">Practice Problems on Hypotenuse<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Hypotenuse in Right Triangle<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Hypotenuse is ______________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">the side adjacent to the right angle<\/div><div class=\"spq_answer_block\" data-value=\"1\">the side opposite the right angle<\/div><div class=\"spq_answer_block\" data-value=\"2\">the shortest side of a right triangle<\/div><div class=\"spq_answer_block\" data-value=\"3\">the side opposite to the smallest angle<\/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 side opposite the right angle<br\/>The hypotenuse is the side that lies opposite to the right angle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the length of the perpendicular of a right triangle whose base is 7 inches and whose hypotenuse is 25 inches.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">22 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">24 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">26 inches<\/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: 24 inches<br\/>Hypotenuse\u00b2 $=$ Base\u00b2 $+$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $=$ Hypotenuse\u00b2 $-$ Base\u00b2<br>\r\nPerpendicular\u00b2 $=  (25)\u00b2 \\;-\\; (7)\u00b2 = 625 \\;-\\; 49 = 576$<br>\r\nPerpendicular\u00b2 $= (24)\u00b2$<br>\r\nPerpendicular $= 24$ inches.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The longest side of the right-angled triangle is called ____________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">base<\/div><div class=\"spq_answer_block\" data-value=\"1\">perpendicular<\/div><div class=\"spq_answer_block\" data-value=\"2\">hypotenuse<\/div><div class=\"spq_answer_block\" data-value=\"3\">leg<\/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: hypotenuse<br\/>Hypotenuse is the longest side of the right-angled triangle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">In the following image, a and b are ____.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-1-8.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">equal<\/div><div class=\"spq_answer_block\" data-value=\"1\">legs<\/div><div class=\"spq_answer_block\" data-value=\"2\">diagonals<\/div><div class=\"spq_answer_block\" data-value=\"3\">hypotenuses<\/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: legs<br\/>In right triangles, the base and the perpendicular are also called legs.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find AC.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-2-4.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">AC $= 20$ feet<\/div><div class=\"spq_answer_block\" data-value=\"1\">AC $= 22$ feet<\/div><div class=\"spq_answer_block\" data-value=\"2\">AC $= 24$ feet<\/div><div class=\"spq_answer_block\" data-value=\"3\">AC $= 26$ feet<\/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: AC $= 26$ feet<br\/>AC $= \\sqrt{(AB)\u00b2 + (BC)\u00b2}$<br>\r\nAC $= \\sqrt{(24)\u00b2 + (10)\u00b2}$<br>\r\nAC $= \\sqrt{(576 + 100)} = \\sqrt{676} = 26$ feet.<\/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\": \"Hypotenuse in Right Triangle\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Hypotenuse in Right Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Hypotenuse is ______________.\",\n                    \"text\": \"Hypotenuse is ______________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"the side adjacent to the right angle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"the shortest side of a right triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"the side opposite to the smallest angle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"the side opposite the right angle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The hypotenuse is the side that lies opposite to the right angle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the length of the perpendicular of a right triangle whose base is 7 inches and whose hypotenuse is 25 inches.\",\n                    \"text\": \"Find the length of the perpendicular of a right triangle whose base is 7 inches and whose hypotenuse is 25 inches.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"22 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"26 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"24 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Hypotenuse\u00b2 $$=$$ Base\u00b2 $$+$$ Perpendicular\u00b2<br>\r\nSo, Perpendicular\u00b2 $$=$$ Hypotenuse\u00b2 $$-$$ Base\u00b2<br>\r\nPerpendicular\u00b2 $$=  (25)\u00b2 \\\\;-\\\\; (7)\u00b2 = 625 \\\\;-\\\\; 49 = 576$$<br>\r\nPerpendicular\u00b2 $$= (24)\u00b2$$<br>\r\nPerpendicular $$= 24$$ inches.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The longest side of the right-angled triangle is called ____________.\",\n                    \"text\": \"The longest side of the right-angled triangle is called ____________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"base\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"leg\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"hypotenuse\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Hypotenuse is the longest side of the right-angled triangle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the following image, a and b are ____.\",\n                    \"text\": \"In the following image, a and b are ____. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-1-8.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"equal\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"diagonals\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"hypotenuses\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"legs\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In right triangles, the base and the perpendicular are also called legs.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find AC.\",\n                    \"text\": \"Find AC. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-2-4.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AC $$= 20$$ feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AC $$= 22$$ feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"AC $$= 24$$ feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"AC $$= 26$$ feet\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"AC $$= \\\\sqrt{(AB)\u00b2 + (BC)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(24)\u00b2 + (10)\u00b2}$$<br>\r\nAC $$= \\\\sqrt{(576 + 100)} = \\\\sqrt{676} = 26$$ feet.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-hypotenuse\">Frequently Asked Questions on Hypotenuse<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b5509452-0d35-4e8d-8c3e-a8957685c520\" 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-b5509452-0d35-4e8d-8c3e-a8957685c520\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b5509452-0d35-4e8d-8c3e-a8957685c520\"><strong>What is the similar triangle theorem?<\/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-b5509452-0d35-4e8d-8c3e-a8957685c520\">\n\n<p class=\"eplus-wrapper\">The similar triangle theorem states that two triangles are similar when their corresponding angles are congruent, and their sides are proportionately 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-b5509452-0d35-4e8d-8c3e-a8957685c520\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b5509452-0d35-4e8d-8c3e-a8957685c520\"><strong>Can you find the hypotenuse of other triangles other than the right triangle?<\/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-b5509452-0d35-4e8d-8c3e-a8957685c520\">\n\n<p class=\"eplus-wrapper\">No. In geometry, the hypotenuse is only defined for right-angled triangles and not for any other type of triangle.<\/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-b5509452-0d35-4e8d-8c3e-a8957685c520\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b5509452-0d35-4e8d-8c3e-a8957685c520\"><strong>What are the sides of a right triangle collectively called?<\/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-b5509452-0d35-4e8d-8c3e-a8957685c520\">\n\n<p class=\"eplus-wrapper\">The sides of a right triangle are collectively known as Pythagorean triplets.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Hypotenuse? A right-angled triangle is a triangle that has one interior angle, which measures 90 degrees. The side opposite to the right angle in a right-angled triangle is known as the hypotenuse. It is the longest side. Definition of Hypotenuse? The sides of a right triangle are base, perpendicular, and hypotenuse. As &#8230; <a title=\"Hypotenuse in Right Triangle &#8211; Definition, Formula\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/hypotenuse\" aria-label=\"More on Hypotenuse in Right Triangle &#8211; Definition, Formula\">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-25413","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\/25413","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=25413"}],"version-history":[{"count":15,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25413\/revisions"}],"predecessor-version":[{"id":37393,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25413\/revisions\/37393"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}