Question

A circle is inscribed within an equilateral triangle of area √3 sqm. The circumference of the circle will be ?

Answer 1

Let radius of circle is r .
we know, radius of inscribed circle is given by
r = ∆/s , here ∆ is area of triangle and s is semiperimeter of triangle .

Given, area of triangle , ∆ = √3 m²
Given an equilateral ,
∴ all sides are equal . Let side length = x
so, area of triangle = √3/4 × x²
√3 = √3/4 × x²
x = 2 m
Now, Semiperimeter of triangle , s = (2 + 2 + 2)/2 = 3m

Now, radius of inscribed circle , r = √3/3 = 1/√3 m
∴ circumference = 2πr = 2π/√3 m