What is the approximate area of the triangle ABC?
Consider the following for the next two (02) items that follow :<br>The perimeter of a triangle ABC is 105 cm. The altitudes AD, BE and CF are in the ratio 3:5:6.
- A. 175 square cm
- B. 190 square cm
- C. 205 square cm
- D. 285 square cm ✓
Correct Answer: D. 285 square cm
Explanation
The sides are 5x, 10x, 6x. Perimeter 21x = 105 \implies x = 5. The sides are 25, 50, 30. Semi-perimeter s = 52.5. By Heron's formula, Area = \sqrt{52.5(52.5-25)(52.5-50)(52.5-30)} = \sqrt{52.5 \times 27.5 \times 2.5 \times 22.5} \approx \sqrt{81211} \approx 285 sq cm.
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