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The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is?

Correct Answer: 126 cms

Explanation:

∵ 22/7 x r2 = 462
⇒ r2 = (462 x 7) /22 = 147
⇒ r = 7√3 cm
∴ Height of the triangle = 3r = 21√3 cm
Now, ∵ a2 = a2/4 + (3r)2
⇒ 3a2/4 = (21√3)2
⇒ a2 = (1323 x 4)/3
⇒ a = 21x 2 = 42 cm
∴ Perimeter = 3a = 3 x 42
=126 cm


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