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.

shreyas1
Oct 4, 2018

#1**+1 **

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

CPhill
Oct 4, 2018