Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If each side of a square is increased by 25%, find the percentage change in its area.
Answer
Answer (as printed):
Explanation
Let each side of the square be $a$. Then, area $=a^{2}$. $$\text { New side }=\frac{125 a}{100}=\frac{5 a}{4} \text {. New area }=\left(\frac{5 a}{4}\right)^{2}=\frac{25 a^{2}}{16} \text {. }$$ $$\begin{aligned} & \text { Increase in area }=\left(\frac{25 a^{2}}{16}-a^{2}\right)=\frac{9 a^{2}}{16} . \\ & \therefore \text { Increase } \%=\left(\frac{9 a^{2}}{16} \times \frac{1}{a^{2}} \times 100\right) \%=56.25 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.