The sides of a right-angled triangular park are in the ratio 5 : 12 : 13. If the sum of all sides is 120 meters. What is the area…

Question

The sides of a right-angled triangular park are in the ratio 5 : 12 : 13. If the sum of all sides is 120 meters.

What is the area of the park?

1. A. 520 m²
2. B. 480 m² (Correct answer)
3. C. 120 m²
4. D. 360 m²

Correct Answer

Option B — 480 m²

Detailed Solution & Explanation

The correct answer is 480 m².

Key Points

• The sides are in the ratio 5 : 12 : 13, a total of 30 parts.
• The perimeter is 120 m, so one part = 120 ÷ 30 = 4 m, giving sides of 20 m, 48 m and 52 m.
• Since 5-12-13 is a Pythagorean triple, the legs are 20 and 48 and the hypotenuse is 52.
• Area = ½ × 20 × 48 = 480 m².

Additional Information

• Verify the right angle: 20² + 48² = 400 + 2304 = 2704 = 52² ✓
• In any right triangle the two legs serve directly as base and height, so no separate altitude calculation is needed.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*