If each side of a square is increased by 25% Then the percentage change in its area is - Maths - Area and Perimeter

Question

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

Poonam Mittal · Accepted Answer

Let the side of the square be a

Area of the square = (a)²

Increased side

$a + \frac{25}{100} a = \frac{5 a}{4}$

Area = ${(\frac{5 a}{4})}^{2} = \frac{25 a^{2}}{16}$

% increase in area

$\frac{\frac{25 a^{2}}{16} - a^{2}}{a^{2}} \times 100 = \frac{\frac{25 a^{2} - 16 a^{2}}{16}}{a^{2}} \times 100 = \frac{9 a^{2}}{16 a^{2}} \times 100 = \frac{225}{4} %$

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