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

(d) 56.25%

Let the side of the square be a cm.
Area of the square = (a)² cm²
Increased side = (a + 25% of a) cm
= $\left(a+\frac{25}{100}a\right)$ cm = $\left(a+\frac{1}{4}a\right)\mathrm{cm}=\left(\frac{5}{4}a\right)$ cm
Area of the square = ${\left(\frac{5}{4}a\right)}^{2}c{\mathrm{m}}^2=\left(\frac{25}{16}{a}^2\right)$ cm²
Increase in the area = $\left[\left(\frac{25}{16}{a}^2\right)-a^2\right]$ cm²= $\left(\frac{25a^2-16a^2}{16}\right)$ cm² = $\left(\frac{9a^2}{16}\right)$ cm²
% increase in the area = $\frac{\mathrm{Increased}\mathrm{area}}{\mathrm{Old}\mathrm{area}}\times 100$
= $\left[\frac{\left({\displaystyle \frac{9}{16}}{a}^2\right)}{a^2}\times 100\right]$ = $\left(\frac{9\times 100}{16}\right)=56.25$