Question : If the ratio of the area of two similar triangles is $\sqrt{3}:\sqrt{2}$, then what is the ratio of the corresponding sides of the two triangles?
Option 1: 9 : 4
Option 2: 3 : 2
Option 3: $\sqrt[3]{3}: \sqrt[3]{2}$
Option 4: $\sqrt[4]{3}: \sqrt[4]{2}$
Correct Answer: $\sqrt[4]{3}: \sqrt[4]{2}$
Solution :
Given, that the ratio of the area of two similar triangles is $\sqrt{3}: \sqrt{2}$
We know that the ratio of the area of two similar triangles is equal to the ratio of squares of the corresponding sides of the two triangles.
So, the ratio of squares of the corresponding sides of the two triangles = $\sqrt{3}: \sqrt{2}$
⇒ The ratio of the corresponding sides of the two triangles = $\sqrt[4]{3}: \sqrt[4]{2}$
Hence, the correct answer is $\sqrt[4]{3}: \sqrt[4]{2}$.
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