Quantitative Aptitude Ques 2049
Question: If two medians BE and CF of a $ \Delta ABC, $ intersect each other at G and if $ BG=CG, $ $ \angle BGC=60{}^\circ , $ $ BC=8cm, $ then area of the $ \Delta ABC $ is
Options:
A) $ 96\sqrt{3}cm^{2} $
B) $ 48\sqrt{3}cm^{2} $
C) $ 48cm^{2} $
D) $ 64\sqrt{3}cm^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- Given, $ BG=GC, $ $ BC=8cm $ Let $ \angle GBC=\angle GCB=x $ $ \angle BGC+\angle GCB+\angle CBG=180{}^\circ $
$ \Rightarrow $ $ 60{}^\circ +x+x=180{}^\circ $
$ \Rightarrow $ $ 2x=120{}^\circ $
$ \Rightarrow $ $ x=60{}^\circ $
$ \therefore $ $ \Delta BCG $ Is an equilateral triangle as all the angles are $ 60{}^\circ . $ Area of $ \Delta BCG=\frac{\sqrt{3}}{4}\times 8^{2}=\frac{\sqrt{3}}{4}\times 8\times 8=16\sqrt{3}cm^{2} $
$ \therefore $ Area of $ \Delta ABC=3\times \Delta BCG=3\times 16\sqrt{3}=48\sqrt{3}cm^{2} $
BETA
