Question

By what percentage will the area of a square change if its side increases by $10$%?

Answer 1

Let the original side of the square be $a$ units

Now, original area $=a^2$ sq. units

New side of the square $=a-10\%\times a=a-0.1a=0.9a$

New Area $=0.9\times 0.9a^2=0.81a^2$

Decrease in area $=a^2-0.81a^2=0.19a^2$

Percentage decrease $=\frac{0.19a^2}{a^2}\times 100\%=19\%$