Exams › SSC CGL (Prelims) › General

A right triangle has sides 5, 12, and 13. A smaller similar triangle is inscribed with a perimeter of 10. What is its area?

1. 2.5
2. 3.33
3. 5
4. 7.5

Correct answer: 3.33

Solution

The original right triangle has perimeter \(5+12+13=30\). The smaller similar triangle has perimeter 10, so the scale factor is \(10/30=1/3\). The original area is \(\frac{1}{2}\times 5\times 12=30\), so the smaller area is \(30\times (1/3)^2=10/3\approx 3.33\).

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