Question
The area of a circle inscribed in a equilateral triangle is 154 `cm^2` . Find the perimeter of the triangle .
Answer: Option D
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Radius of incircle = `(a)/(2sqrt(3))`.
Area of incircle = `((pi xx a^2)/(12)) cm^2`
`:.` ` (pi a^2)/(12) = 154`
`hArr a^2 = (154 xx 12 xx 7)/(33)`
`hArr a = 14sqrt(3)`
`:.` Perimeter of the triangle = `(3 xx 14sqrt(3)` cm
= (42 x 1.732) cm = 72.7 cm( approx).
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