ABC26GN4494 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the side of an equilateral triangle is decreased by 20\%, its area is decreased by
(a)36\%
(b)40\%
(c)60\%
(d)64\%
Answer
Explanation
Let the sides be $x \mathrm{cm}$ and (80\% of $x) \mathrm{cm}=\frac{4 x}{5} \mathrm{cm}$. Then, initial area $$=\frac{\sqrt{3}}{4} x^{2}, \text { final area }=\frac{\sqrt{3}}{4} \cdot\left(\frac{4 x}{5}\right)^{2}=\frac{16 \sqrt{3} x^{2}}{100} .$$ Decrease in area $=\left(\frac{\sqrt{3}}{4} x^{2}-\frac{16 \sqrt{3}}{100} x^{2}\right) \mathrm{cm}^{2}=\frac{9 \sqrt{3} x^{2}}{100} \mathrm{cm}^{2}$. $$\text { Decrease } \%=\left(\frac{9 \sqrt{3} x^{2}}{100} \times \frac{4}{\sqrt{3} x^{2}} \times 100\right) \%=36 \% .$$
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