Question

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

Answer 1

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`