The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2√3]
Where, a be the length of the side of an equilateral triangle.
Given that, area of a circle inscribed in an equilateral tringle = 154 cm²
∴ π(a/2√3)² = 154
⇒ (a/2√3)² = 154 x (7/22) = (7)a²
⇒ a = 42√3 cm
Perimeter of an equilateral triangle = 3a
= 3(14√3)
= 42√3 cm