If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60°, BC = 8 cm, then area of the triangle ABC is:

A. $$96\sqrt 3 $$  cm²

B. $$48\sqrt 3 $$  cm²

C. 48 cm²

D. $$54\sqrt 3 $$  cm²

Answer: Option B

Solution(By Examveda Team)

According to question,
⇒ ∵ ∠BGC = 60° (given)
⇒ ∠GBC = ∠GCB = x°
⇒ x° + x° + 60° = 180°
⇒ x = 60°

⇒ So ΔBGC is an equilateral triangle with side 8 cm each
Then,
Area pf triangle ΔBGC
= $$\frac{{\sqrt 3 }}{4}$$ a²
= $$\frac{{\sqrt 3 }}{4}$$ 8²
= 16$${\sqrt 3 }$$ cm²
⇒ Area of ΔABC
= Area (ΔBGC + ΔAGC + ΔAGB)
⇒ Area of ΔABC = 3 × 16$${\sqrt 3 }$$
⇒ Area of ΔABC = 48$${\sqrt 3 }$$ cm² {∵ ΔBGC = ΔAGC = ΔAGB}