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 :

Answer: Option D

Let the sides of the rectangle be x metres and (x + 48) metres
Then,
$$\begin{array}{rl}& 2\left(x+x+48\right)=160\\ & \Rightarrow 4x+96=160\\ & \Rightarrow 4x=64\\ & \Rightarrow x=16\end{array}$$
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