The sides of similar triangle △ ABC and △ DEF are in the ratio of (√(3))/(√(5)) of △ DEF (in cm²) is:: If the area of △ ABC is 90 cm², then the area

The sides of similar triangle △ ABC and △ DEF are in the…

The sides of similar triangle $\triangle$ ABC and $\triangle$ DEF are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$ of $\triangle$ DEF (in cm²) is:: If the area of $\triangle$ ABC is 90 cm², then the area

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 150.

Given that

The sides ratio of the similar triangles $\triangle$ ABC and $\triangle$ DEF = $\frac{\sqrt{3}}{\sqrt{5}}$

If the area of $\triangle$ ABC is 90 cm²,

Formula used

Area of $\triangle$ DEF/Area of $\triangle$ ABC = (sides of $\triangle$ DEF/sides of $\triangle$ DEF)²

Calculation

Area of $\triangle$ DEF/90 = ( $\frac{\sqrt{5}}{\sqrt{3}}$ )² = 5/3

Area of $\triangle$ DEF = 90 × 5/3 = 150 cm²

SSC CHSL 2023 PYQ — Question 65