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SSC CGL 2018 PYQ — Question 99

SSC CGL Tier II Quant - 09/03/2018 • Quantitative Aptitude • Q99

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An equilateral triangle of side 12 cm is drawn. What is the area (in cm2) of the largest square which can be drawn inside it?

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Correct answer: B

Explanation

  The correct answer is option 2 i.e. 3024 − 1728√3

Application

Side of the equilateral triangle ABC = 12 cm

In the figure:

∠ACB = 60°

So,

RC = 2/√3 × a

So,

AC = AR + RC = a + 2a/√3

⇒ a(1 + 2/√3) = 12

⇒ a(√3 + 2) = 12√3

⇒ a = 12√3/(2 + √3)

⇒ a = 12√3 (2 – √3) = (24√3 – 36) cm

Hence,

Area of the square = (24√3 – 36)2

= 1728 + 1296 – 1728√3

= 3024 − 1728√3