Perimeter of a rectangle - Definition with Examples

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Perimeter of a Rectangle

Rectangles are four-sided polygons. Following are the properties of a rectangle:

(i) All the angles of a rectangle are 90º.

(ii) Opposite sides of a rectangle are always the same in size.

Properties of a Rectangle

 

Perimeter of a rectangle

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle.

Perimeter of a rectangle

Perimeter of the given rectangle is a + b + a + b. Since opposite sides of a rectangle are always equal, we need to find the dimensions of only two sides to find the perimeter of a rectangle.

The perimeter of the above rectangle with sides ‘a units’ and ‘b units’ is: 

 a + b + a + b = 2a + 2b = 2  (a + b) units.

Hence, the formula for the perimeter of a rectangle = 2 × (sum of adjacent sides)

 

Examples of finding the perimeter of a rectangle

Example 1. The two sides of the rectangle are given. What will be the perimeter of the rectangle?

Find the Perimeter of a rectangle

Solution: One side of the rectangle is 2 cm and the other side is 5 cm.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangle = 2 × (5 + 2) = 2 × (7) = 14 cm

 

Example 2. A rectangular playground is 20 m long and 13 m wide. Find its perimeter.

Find the Perimeter of a rectangle

Solution: One side of the rectangular playground is 20 m and the other side is 13 m.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

Therefore, the perimeter of the rectangular ground = 2 × (20 + 13) = 2 × (33) = 66 m

 

Tricky problems involving perimeter of rectangles

Type I: When the perimeter and only one of the sides are given.

Example 1. If the perimeter of the given rectangle is 10 cm and the length of one of its sides is 2 cm. What will be the other side?

Perimeter of rectangles problems

Solution: The perimeter of the rectangle, with one of the sides equal to 2 cm, is 10 cm.

Let the missing side be ‘a’.

We know that, the perimeter of a rectangle = 2 × (sum of adjacent sides)

10 = 2 × (2 + a) 5 = (2 + a)

       a = 5 - 2 = 3 cm

 

Type II: Finding sides using the properties of a rectangle.

Example 2. In the given rectangle, if  a = 4 cm and d = 3 cm. Find b and c.

Finding sides using the properties of a rectangle

Solution: We know  that side a = 4 cm and side d = 3 cm.

To find side b and c, we use the property that the opposite sides of a rectangle are always the same in size.

 Finding sides using the properties of a rectangle

Hence, a = c = 4 cm and d = b = 3 cm.

  Fun Facts

  • Many historical buildings have rectangle like shapes in them e.g. Parthenon in Athens.

 

Frequently Asked Questions

  • What is the formula to find the perimeter of a rectangle?

    Perimeter of a Rectangle = 2 × (Length + Width)

  • How can you find the length of a rectangle with the given width and perimeter?

    Perimeter of Rectangle = 2 (Length + Width) Rearranging the terms in this formula, we get, 1/2 x (Perimeter) – Width = Length So, to find the length of a rectangle, subtract the width from half of the perimeter.

  • Can two different rectangles have the same perimeter?

    Yes, different rectangles can have the same perimeter. For example: Rectangle 1: Length (l1) = 5 cm, Width (w1) = 6 cm Perimeter = Perimeter = 2 × (l1 + w1) = 2 × (5 cm + 6 cm) = 22 cm Rectangle 2: Length (l2) = 3 cm, Width (w2) = 8 cm Perimeter = Perimeter = 2 × (l2 + w2) = 2 × (3 cm + 8 cm) = 22 cm

  • Which unit of measurement is used to measure the perimeter of a rectangle?

    Perimeter of a rectangle is measured in the same unit as the length and width of the rectangle. For example, the units of measurements can be centimeters, meters, feet, yards, etc.

Practice Problems on Perimeter Of A Rectangle

Pick the correct answer
1.   The sum of length and width of a rectangle is 12 units. What is its perimeter?
2.   What is the perimeter of a rectangle with a length of 10 cm and a width of 5 cm?
3.   The length of a rectangle is twice its width. If the width of the rectangle is 4 units, what is the perimeter of the rectangle?
4.   The perimeter of a rectangle is 12 cm. If the length of the rectangle is 4 cm, what is the width of the rectangle?
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