Question : The sides of similar triangle $\triangle ABC$ and $\triangle DEF$ are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$. If the area of $\triangle ABC$ is $90 \text{ cm}^2$, then the area of $\triangle DFF\left(\right.$ in $\left.\text{cm}^2\right)$ is:
Option 1: 150
Option 2: 152
Option 3: 154
Option 4: 156
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Correct Answer: 150
Solution :
Ratio of their sides = $\frac{\sqrt3}{\sqrt5}$
$\therefore$ Ratio of their areas = $(\frac{\sqrt3}{\sqrt5})^2 = \frac{3}{5}$
Given the area of $\triangle ABC$ = $90\text{ cm}^2$
$\therefore$ Area of $\triangle DEF=90\times \frac{5}{3} = 150\text{ cm}^2$
Hence, the correct answer is 150.
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