The radius of a circle inscribed in a regular triangle is 12√3 cm. Find the perimeter of the triangle.

It is known that the radius of a circle inscribed in a regular triangle is 12√3 cm. You need to find the perimeter of the triangle.

So, a regular triangle is an equilateral triangle (the sides of which are equal to each other).

Let’s recall the formula for finding the radius of a circle inscribed in an equilateral triangle:

r = a / 2√3;

Substitute the value for the radius and find the value for the side of the triangle:

12√3 = a / 2√3;

a = 12√3 * 2√3 = 24 * 3 = 72 cm;

So, the side length is known.

Find the perimeter of the triangle P = 3a = 3 * 72 = 216 cm.

Answer: 216 cm.