# A triangle has sides with lengths of 3, 9, and 8. What is the radius of the triangles inscribed circle?

##### 1 Answer

Mar 5, 2016

Heron's formula states that

Area =

Where s is the sum of all sides / 2 (Also known as the semiperimeter)

a,b,c are the side lengths

From here, you can just plug in all the values.

Find that s = 10

Area =

Get

Now, we use the formula that says that

Area = semiperimeter * inradius

So we have

Therefore, the radius is

We can simplify the radical and cancel out to get