What is the radius of the circle inscribed in triangle ABC if AB = 10, AC = 17, BC = 21? Express your answer as a decimal to the nearest tenth.

shreyas1
Oct 7, 2018

#1**+1 **

We can find the area of this triangle using Heron's Formula

s = [ 10 + 17 + 21 ] / 2 = 48 / 2 = 24

The area = √ [ s (s - 10) (s - 17) (s - 21) ] =

√ [ 24 (14) (7) (3) ] =

√7056 = 84 units^2

The area = 1/2 [ sum of triangle's sides ] * altitude of each triangle

But....the altitude of each triangle = the radius of the incircle

So...we have

84 = (1/2) (48) * radius of incircle

84 = 24 * radius of incircle

84 / 24 = rasius of incircle = 3.5 units

EDIT TO CORRECT AN ERROR !!!!

CPhill
Oct 7, 2018