Question

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

(a) 25% (b) 55% (c) 55.5% (d) 56.25%

Answer 1

Let a be the side of the square. Then
Side of the new square = a + 25% of a = $a+a\times \frac{25}{100}=\frac{5a}{4}$
Old area = a²
New area = ${\left(\frac{5a}{4}\right)}^2=\frac{25a^2}{16}$
% increase in the area = $\frac{\mathrm{Change}\mathrm{in}\mathrm{area}}{\mathrm{Old}\mathrm{area}}\times 100=\frac{{\displaystyle \frac{25a^2}{16}}-a^2}{a^2}\times 100=\frac{9}{16}\times 100=56.25$
Hence, the correct option is (d).