SATHEE: Quantitative Aptitude Ques 825

Quantitative Aptitude Ques 825

Question: If the length of each side of an equilateral triangle is increased by 2 units, the area is found to be increased by $ 3+\sqrt{3} $ sq units. The length of each side of the triangle is

Options:

A) $ \sqrt{3}units $

B) $ 3\sqrt{3}units $

C) $ 3units $

D) $ 1+3\sqrt{3}units $

Show Answer

Answer:

Correct Answer: A

Solution:

Let the original side of equilateral triangle be x units New length of each side $ =(x+2) $ According to the question, $ \frac{\sqrt{3}}{4}{{(x+2)}^{2}}-\frac{\sqrt{3}}{4}(x^{2})=3+\sqrt{3} $

$ \Rightarrow $ $ \frac{\sqrt{3}}{4}[{{(x+2)}^{2}}-x^{2}]=3+\sqrt{3} $

$ \Rightarrow $ $ \frac{\sqrt{3}}{4}[4x+4]=3+\sqrt{3} $

$ \Rightarrow $ $ 4\sqrt{3}x+4\sqrt{3}=12+4\sqrt{3} $

$ \Rightarrow $ $ 4\sqrt{3}x=12 $ $ x=\frac{12}{4\sqrt{3}}=\sqrt{3} $

Quantitative Aptitude Ques 824

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