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If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60° and BC = 8 cm then area of the triangle ABC is
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- 96√3 cm²
- 64√3 cm²
- 48√3 cm²
- 48 cm²
- 96√3 cm²
Correct Option: C
Using Rule 6,
∠BGC = 60° BG = GC
∴ ∠GBC = ∠GCB = 60°
∴ ∆GBC is an equilateral triangle.
∴ Area of ∆GBC
| = | × 8² | |
| 4 |
= 16√3 sq. cm.
∴ Area of ∆ABC = 3 × 16√3 = 48√3 sq. cm.
