Question

The area of circle inscribed in an equilateral triangle is 154 cm². Find the perimeter of the triangle.

Answer 1

Let the circle inscribed in the equilateral triangle be with a centre O and radius r.

We know that, Area of a Circle = πr²

But, the given that area is 154 cm².

(22/7) × r² = 154

r² = (154 x 7)/22 = 7 × 7 = 49

r = 7 cm

From the figure seen above, we infer that

At point M, BC side is tangent and also at point M, BM is perpendicular to OM.

We know that,

In an equilateral triangle, the perpendicular from vertex divides the side into two halves.

BM = \(\frac{1}{2}\) x BC

Consider the side of the equilateral triangle be x cm.

Therefore, the perimeter of the triangle is found to be 42√3 cm = 42(1.73) = 72.7 cm