Question

A square and a rectangle have the same area. If the length of the rectangle is $25\%$ more than the side of the square, then the breadth of the rectangle is less than the side of the square by:

• A. $20\%$
• B. $25\%$
• C. $33\frac{1}{3}\%$
• D. $50\%$

Answer 1

Answer: (A)

$20\%$

Let the side of the square $=a$ and the breadth of the rectangle is $x\%$ less than the side of the square.

Breadth of the rectangle $=a\left(1-\frac{x}{100}\right)$

Length of the rectangle $=a\left(1+\frac{25}{100}\right)$

$=a\times \frac{125}{100}$

$=a\times \frac{5}{4}$

Area of the rectangle = Area of the square {Given}

$\Rightarrow \frac{5}{4}a\times a\left(1-\frac{x}{100}\right)=a\times a$

$\Rightarrow \frac{(100-x)}{80}=1$

$\Rightarrow 100-x=80$

$\therefore x=100-80$

$=20$

Hence the breadth of the rectangle is $20$% less than the side of the square.