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

Jun 6, 2018

$r = \frac{\sqrt{15}}{3} \approx 1.29$

#### Explanation:

Here is the formula for a triangle inscribed circle:

$s = \frac{a + b + c}{2}$

$r = \sqrt{\frac{\left(s - a\right) \left(s - b\right) \left(s - c\right)}{s}}$

Plug in our values:

$s = \frac{8 + 4 + 6}{2}$

$s = 9$

$r = \sqrt{\frac{\left(9 - 8\right) \left(9 - 4\right) \left(9 - 6\right)}{9}}$

$r = \sqrt{\frac{5}{3}}$

$r = \frac{\sqrt{15}}{3} \approx 1.29$