Question

The length of a rectangular hall is 5 metres more than its breadth. If the perimeter of the hall is 74 metres, find its length and breadth.

Answer 1

Let the breadth of the hall be x metres.
Then, the length of the hall will be (x + 5) metres.
Perimeter of the hall = 2(Length + Breadth) = 2( x + 5 + x) metres
Given perimeter of the rectangular hall = 74 metres

∴ 2( x + 5 + x) = 74
or, 2 ( 2x + 5 ) = 74
or, 2 ×2x + 2 ×5 = 74 [On expanding the brackets]
or, 4x + 10 = 74
or, 4x + 10 $-$ 10 = 74 $-$ 10 [Subtracting 10 from both the sides]
or, 4x = 64
or, $\frac{4x}{4}=\frac{64}{4}$ [Dividing both the sides by 4]
or, x = 16 metres
∴ Breadth of the park = x
= 16 metres
Length of the park = x + 5 = 16 + 5
= 21 metres