Perimeter of a rectangular field is 160 metres and the difference between its two adjacent sides is 48 metres. The side of a square field, having the same area as that of the rectangle, is :

A. 4 metres

B. 8 metres

C. 16 metres

D. 32 metres

Answer: Option D

Solution(By Examveda Team)

Let the sides of the rectangle be x metres and (x + 48) metres
Then,
$$\eqalign{ & 2\left( {x + x + 48} \right) = 160 \cr & \Rightarrow 4x + 96 = 160 \cr & \Rightarrow 4x = 64 \cr & \Rightarrow x = 16 \cr} $$
So, sides of the rectangle are 16 metres and 64 metres
Area of the rectangle :
= (16 × 64) m²
= 1024 m²
Area of the square = 1024 m²
∴ Side of the square :
= $$\sqrt {1024} $$  m
= 32 metres