# A triangle has sides with lengths of 6, 4, and 2. What is the radius of the triangles inscribed circle?

Jan 21, 2016

$0$

#### Explanation:

Since the sum of the two shorter sides is equal to the length of the longest side, the triangle is flat.

For a general solution to this type of problem:

A triangle with sides $a , b , c$ and semiperimeter $s = \frac{a + b + c}{2}$

has an area given by Heron's Formula as

$A r e {a}_{\triangle} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

and inscribed circle radius of

$r a \mathrm{di} u {s}_{\triangle} = \frac{A r e {a}_{\triangle}}{s}$