Question

On increasing each side of a square by 25% , the increase in area will be _____________.

• A. 25%
• B. 55%
• C. 40.5%
• D. 56.25%

Answer 1

The correct option is D 56.25%

Let the Side of Square be $x$

Then,

Initial area of Square = $x^2$

According to Question

Side is increased by $25\%$

New Side $=x+25\%ofx$

$\to x+\frac{x}{4}$

$\to \frac{5x}{4}$

New Area $=(\frac{5x}{4}{)}^2$

$\to \frac{25x^2}{16}$

Percentage increase in area$=\frac{\frac{25x^2}{16}-x^2}{x^2}\times 100=\frac{9}{16}\times 100=56.25\%$

Thus, Correct answer is $D$