A triangle has sides with lengths of 6, 9, and 8. What is the radius of the triangles inscribed circle?

1 Answer
Anthony X
Feb 10, 2016

You should use Heron's formula to find this answer
Find the semiperimeter, which is 11.5
Use Heron's to get Area = #sqrt(11.5*5.5*2.5*3.5)#
inradius is #sqrt(8855)/46#

Explanation:

First find the semiperimeter which is the sum of the sides over 2
This is 11.5

Use this to plug into Heron's formula to get
#sqrt((23/2)(11/2)(5/2)(7/2))#
Simplify to get #sqrt(8855)/4# as the Area

Now use the formula
Area = inradius * semiperimeter
#sqrt(8855)/4# = r * 11.5

#sqrt(8855)# = 46r

Thus r = #sqrt(8855)/46#

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