Quantitative Aptitude Ques 1946

Question: Two vertices of an equilateral triangle are origin and (4, 0). What is the area of the triangle?

Options:

A) $ 4 $ sq units

B) $ \sqrt{3} $ sq units

C) $ 4\sqrt{3} $ sq units

D) $ 2\sqrt{3} $ sq units

Show Answer

Answer:

Correct Answer: C

Solution:

  • Since, triangle is equilateral.

$ \therefore $ $ AB=BC=CA $
$ \Rightarrow $ $ BD=\frac{4}{2}=2 $ In $ \Delta ADC, $ $ AD^{2}=4^{2}-2^{2}=16-4=12 $

$ \Rightarrow $ $ AD=2\sqrt{3} $

$ \therefore $ Area of $ \Delta ABC=\frac{1}{2}\times BC\times AD=\frac{1}{2}\times 4\times 2\sqrt{3} $ $ =4\sqrt{3},squnits $

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