Question : If the ratio of corresponding sides of two similar triangles is $\sqrt{5}: \sqrt{7},$ then what is the ratio of the area of the two triangles?
Option 1: $\sqrt[3]{5}: \sqrt{7}$
Option 2: $25: 49$
Option 3: $\sqrt{5}: \sqrt{7}$
Option 4: $5: 7$
Correct Answer: $5: 7$
Solution :
Given, the ratio of sides of similar triangles = $\sqrt{5}: \sqrt{7}$
We know the ratio of areas of similar triangles is equal to the square of the ratio of sides of those similar triangles
$\therefore$ Ratio of areas of similar triangles = $(\sqrt{5})^2: (\sqrt{7})^2=5 : 7$
Hence, the correct answer is $5 : 7$.
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