The radius of a circle inscribed in an equilateral triangle is 2√3 cm find the perimeter of the triangle

Let x denote the side length of this equilateral triangle.

Then the area S of this triangle should be equal to:

S = x * x * sin (60 °) / 2 = x ^ 2 * (√3 / 2) / 2 = x ^ 2 * √3 / 4 cm ^ 2,

the perimeter p of this triangle should be 3 cm.

According to the condition of the problem, the radius of the circle inscribed in this equilateral triangle is 2√3 cm.

Using the formula for the area of ​​a triangle in terms of the radius of the inscribed circle, we can compose the following equation:

x ^ 2 * √3 / 4 = 2√3 * 3x / 2,

solving which, we get:

x ^ 2 * √3 / 4 = x * 3√3;

x = 3√3 * 4 / √3;

x = 12 cm.

Find the perimeter of this triangle:

3x = 3 * 12 = 36 cm.

Answer: 36 cm.