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Length of the perpendiculars from a point in the interior of an equilateral triangle on its sides are 3 cm, 4 cm and 5 cm. Area of the triangle is
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- 48√3 cm²
- 54√3 cm²
- 72√3 cm²
- 80√3 cm²
- 48√3 cm²
Correct Option: A
Using Rule 1 and 6, A
Let the side of the equilateral triangle be x cm.
∴ ∆AOB + ∆BOC + ∆COA = ∆ABC
| ⇒ | x × 3 + | × x × 4 + | × x × 5 = | x² | ||||
| 2 | 2 | 2 | 4 |
| ⇒ 6 = | x ⇒ x = | = 8√3 | ||
| 4 | √3 |
| ∴ Area of ∆ABC = | × side² | |
| 3 |
| = | × 8√3 × 8√3 = 48√3sq. cm. | |
| 4 |
