-
If the length of each median of an equilateral triangle is 6√3 cm, the perimeter of the triangle is
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- 24 cm
- 32 cm
- 36 cm
- 42 cm
- 24 cm
Correct Option: C
If AB = x cm, then
| BC = | cm | |
| 2 |
∴ From ∆ABD AB² = BD² + AD²
| ⇒ x² = | + (6√3)² | |
| 4 |
| ⇒ x² = | = 36 × 3 | |
| 4 |
| ⇒ | = 36 × 3 | |
| 4 |
⇒ x² = 36 × 4
⇒ x = 6 × 2 = 12 cm
∴ Perimeter of equilateral triangle = 3 × 12 = 36 cm
