Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the diagonal of a square is decreased by $15 \%$, find the percentage decrease in its area.
Answer
Answer (as printed):
Explanation
Let the length of the diagonal of the square be $x$. Then, area $=\frac{x^{2}}{2}$. $$\begin{aligned} & \text { New diagonal }=85 \% \text { of } x=\frac{17 x}{20} . \\ & \text { New area }=\frac{1}{2} \times\left(\frac{17 x}{20}\right)^{2}=\frac{289 x^{2}}{800} . \\ & \text { Decrease in area }=\left(\frac{x^{2}}{2}-\frac{289 x^{2}}{800}\right)=\frac{111 x^{2}}{800} . \\ & \therefore \text { Decrease } \%=\left(\frac{111 x^{2}}{800} \times \frac{2}{x^{2}} \times 100\right) \%=27.75 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.