Perimeter of a Rectangle

The longer side of a rectangle is usually called the length, and the shorter side is the breadth.

length = l
breadth = b

Perimeter of rectangle = \( \scriptsize l \: + \: b \: + \: l \: + \: b \\ = \scriptsize l \: + \: l \: + \: b \: + \: b \\ = \scriptsize 2l \: + \: 2b \\ = \scriptsize 2(l \: + \: b) \)

Perimeter of a Rectangle   =   2l  +   2b

Where  l  =  Length
b =  breadth

breadth (b) is also known as width (w)

Example 7.3.1: 

The length of a rectangular room is 8 m, and the width (breadth) is 6 m. Find the perimeter of the room.

Solution:

Length of the room, l = 8 m

Breadth of the room, b = 6 m

Perimeter  =  2 (l  +   b)

Perimeter =  2(8  +  6)

= 2  ×  14

= 28 m 

Example 7.3.2:

A rectangle is 5 m long and 2000 mm wide. Find the perimeter.

Solution:

First, convert to the same unit, so we will convert millimetres to metres. Remember there are 1000 millimetres in 1 metre. 

breadth (b)  =   2000 mm

= 2000 ÷ 1000

= \( \frac{2000}{1000}\: \scriptsize m \\ = \scriptsize 2 \:m \)

breadth (b) = 2 m

length (l) = 5 m

Perimeter  = 2 (l  + b)

= 2 × (5  +  2)

= 2  ×  7

Perimeter = 14 m

Example 7.3.3:

A rectangle has a perimeter of 68 m. Find

a. the length of the rectangle if the breadth is 13 m
b. the breadth of the rectangle if the length is 24 m

Solution

a. Perimeter of a rectangle = 2(l + b)

Perimeter = 68 m

breadth (b) = 13 m

length (l) = ?

∴ \( \scriptsize 68 = 2(l \: + \: 13) \\ \scriptsize 2(l \: + \: 13) = 68 \\ \scriptsize (l \: + \: 13) = \normalsize \frac{68}{2} \\ \scriptsize l \: + \: 13 = 34 \\ \scriptsize l = 34 \: -\:13 \\ \scriptsize l = 21 \: m \)

b. Perimeter of a rectangle = 2(l + b)

Perimeter = 68 m

breadth (b) = ?

length (l) = 24 m

∴ \( \scriptsize 68 = 2(24 \: + \: b) \\ \scriptsize 2(24\: + \: b) = 68 \\ \scriptsize (24 \: + \: b) = \normalsize \frac{68}{2} \\ \scriptsize 24 \: + \: b = 34 \\ \scriptsize b = 34 \: -\:24 \\ \scriptsize b = 10 \: m \)