Question

The 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. $32m$
• B. $8m$
• C. $4m$
• D. $16m$

Answer 1

Answer: (A)

$32m$

$l-b=48m...\left(1\right)$
and $2(l+b)=160$ $\to l+b=80...\left(2\right)$
Adding $\left(1\right)$ and $\left(2\right)$, $2l=128$
$\Rightarrow l=64m\Rightarrow b=16m$
Area of square $=$ Area of rectangle
$=l\times b=(64\times 16)m^2$
$\therefore$ Each side of the square $=\sqrt{64\times 16}m$
$=(8\times 4)m=32m$