The area of circle inscribed in an equilateral triangle

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

1. 42 √ 3 cms
2. 126 cms
3. 72.6 cms
4. 168 cms

Correct Option: B

∵ 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