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A triangle has an area of 480 sq cm and its sides are in the ratio 5 : 12 : 13. What is the perimeter of the triangle?

1. 120 cm
2. 30 cm
3. 150 cm
4. 60 cm

Correct answer: 120 cm

Solution

The ratio 5:12:13 is a Pythagorean triple. Let sides be 5k, 12k, 13k. Area = (1/2)(5k)(12k) = 30k² = 480, so k² = 16, k = 4. Sides: 20, 48, 52. Perimeter = 20+48+52 = 120 cm.

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