+468 What is the radius of the circle inscribed in triangle ABC if AB = 22, AC=12, BC=14? Express your answer in simplest radical form.
+128475 We can find the area of this triangle using Heron's Formula
s = [ 22 + 12 + 14 ] / 2 = 48/2 = 24
The area is given by :
√[ 24 (24 - 22) (24 - 12) (24 - 14) = √ [24 * 2 * 12 * 10 ] = √[48 * 120] = 24√10
Because the radius of the inscribed circle is perpendicular to each side of the triangle...three triangles are formed.......each with a height = to the circle's radius and with bases of 22, 12 and 14 respectively
So...the area of the triangle can be expressed as
Area = (1/2)r [ 22 + 12 + 14] where r is the altitude of each triangle = the radius of the inscribed circle
Solving for r we have
r = 2* Area / [ 22 + 12 + 14 ] =
2 * 24√10 / [ 48] =
48√10 / 48 =
√10 units
