Exams › SSC CGL (Prelims) › General

A right-angled triangle has legs of 9 cm and 12 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 45 cm. What is the area of the second triangle?

1. 216 cm²
2. 324 cm²
3. 405 cm²
4. 486 cm²

Correct answer: 486 cm²

Solution

The first triangle has hypotenuse \(\sqrt{9^2+12^2}=15\). Since the new hypotenuse is 45 cm, the scale factor is \(45/15=3\). The original area is \(\frac12\cdot 9\cdot 12=54\), so the new area is \(54\times 3^2=486\) cm².

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