A triangle has sides with lengths of 8, 4, and 6. What is the radius of the triangle's inscribed circle?

1 Answer
Feb 13, 2016

We can use semiperimeter and Heron's formula

First, we find the semiperimeter, which is the sum of the sides divided by two.

Therefore, #(8+4+6)/2 = 9# which is the semiperimeter

Now, we can use Heron's formula to find the area, which is
#sqrt((s)(s-a)(s-b)(s-c)) = A#

We just plug in values now
#sqrt((9)(9-8)(9-4)(9-6))#

which is
#sqrt((9)(1)(5)(3))#
which is
#sqrt135#

Therefore, #sqrt135 = A#

Now, we can use the formula relating inradii, Area, and semiperimeter

#A = r * s#

Since we found two values, we can just plug in to find the third.
#sqrt135 = r * 9#

#sqrt(135) / 9 = r#

And we are done.