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From a point in the interior of an equilateral triangle, the length of the perpendiculars to the three sides are 6 cm, 8 cm and 10 cm respectively. The area of the triangle is
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- 48 cm²
- 16√3 cm²
- 192√3 cm²
- 192 cm²
- 48 cm²
Correct Option: C
Using Rule 1 and 6,
Let the side of the equilateral triangle ABC be x cm.
According to the question,
| × x × 6 + | × x × 8 + | × x × 10 = | × x² | ||||
| 2 | 2 | 2 | 4 |
| ⇒ 3x + 4x + 5x = | x² | |
| 4 |
| ⇒ | x = 12 | |
| 4 |
| ⇒ x = | = 16√3 cm | |
| √3 |
∴ Area of ∆ ABC
| ⇒ | × (16√3)² = 192√3 cm² | |
| 4 |
