Find the radius of a circle inscribed in a triangle with sides of 20, 20 and 24 cm.

Let us determine what the value of the semi-perimeter will be for a triangle with sides, which are presented in the condition of our problem:

(20 + 20 + 24): 2 = 64: 2 = 32.

We will determine what the value of the area of such a triangle will be, for which we will use Heron’s formula known from the school curriculum:

√ (32 * (32 – 20) * (32 – 20) * (32 – 24)) = √ (32 * 12 * 12 * 8) = 192.

Let’s determine what will be the value of the radius of the circle that was inscribed in such a triangle:

2 * 192 / (64) = 6.

Answer: Its radius is 6 cm.