CDS 2025 · PYQ · Triangle / Heron's Formula · hard
The perimeter of a triangle ABC is 105 cm. The altitudes AD, BE and CF are in the ratio 3 : 5 : 6. What is the approximate area of the triangle ABC?
- A.175 square cm✓ Correct
- B.190 square cm
- C.205 square cm
- D.285 square cm
Sides AB : BC : CA = 5 : 10 : 6. Let sides be 5k, 10k, 6k. Perimeter = 21k = 105, so k = 5. Sides: 25, 50, 30. Semi-perimeter s = 52.5. By Heron's: Area = √[52.5 × 27.5 × 2.5 × 22.5] = √[52.5 × 27.5 × 56.25] = √81210.94 ≈ 285 sq cm. Hmm let me recompute: 52.5 × 27.5 = 1443.75; 1443.75 × 2.5 = 3609.375; 3609.375 × 22.5 = 81210.94. √81210.94 ≈ 285. So answer (d) 285 sq cm.
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