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lf two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG,
\( \angle BGC = 60 ^{\circ} \), BC = 8 cm, then area of the triangle ABC is:


A) \( 48 cm^{2} \)

B) \( 64\sqrt{3} cm^{2} \)

C) \( 96\sqrt{3} cm^{2} \)

D) \( 48\sqrt{3 cm^{2}} \)

Correct Answer:
D) \( 48\sqrt{3 cm^{2}} \)

Description for Correct answer:





Given : BG = CG; \( \angle BGC = 60 ^{\circ} ; BC = 8 cm \)

Consider Triangle GBC

BG = GC

\( \angle GBC = \angle GCB = 60 ^{\circ} \)

Therefore, Area of Triangle GBC = \( \Large \frac{\sqrt{3}}{4} \left(a\right)^{2} \left(equlateral triangle\right) \)

= \( \Large \frac{\sqrt{3}}{4} \left(8x8\right)=16\sqrt{3}cm^{2} \)

Therefore, Area of Triangle ABC = \( 3 \times 16\sqrt{3} = 48\sqrt{3} cm^{2} \)


Part of solved SSC Practice test(1) questions and answers : Exams >> SSC Exams >> SSC Practice test(1)




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