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