Question

If the area of a rectangle is equal to the area of a square and the length of the rectangle is equal to the perimeter of the square, then the breadth of the rectangle is

• A. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
• B. $\raisebox{1ex}{${\mathrm{side}}^2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
• C. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
• D. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

Answer 1

The correct option is C

$\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

Find the breadth of the rectangle

Let $l$ be the length and $b$ be the breadth of the rectangle.

Area of rectangle $=l\times b$

Area of square$={\mathrm{side}}^2$

Given that, the area of a rectangle is equal to the area of a square.

So,

$l\times b={\mathrm{side}}^2.........\left(1\right)$

Also given that the length of the rectangle is equal to the perimeter of the square

So

$l=4\times \mathrm{side}............\left(2\right)$

Putting $\left(2\right)$ in $\left(1\right)$ we get

$$\begin{gathered} 4\times \mathrm{side}\times b={\mathrm{side}}^2 \\ \Rightarrow 4\times b=\mathrm{side} \\ \Rightarrow \mathrm{b}=\frac{\mathrm{side}}{4} \end{gathered}$$

Hence, the breadth is $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, so, the correct option is (C).