If each side of a square is increased by 25%, find the percentage change in its area.

A 56.25%

B 36.25%

C 16.25%

D 12.25%

Correct Answer: Option A

Let each side of the square be a. Then, area = \(a^2\)

New side = \(\frac{125a}{100}=\frac{5a}4\)

New area = \(\left(\frac{5a}4\right)^2\) = \(\left(\frac{25a^2}{16}\right)\)

Increase in area = \(\frac{25a^2}{16}-a^2=\frac{9a^2}{16}\)

Increase% = \(\left[\frac{9a^2}{16}\ast\frac1{a^2}\ast100\right]\)%

= 56.25%.