# A triangle has sides with lengths of 2, 7, and 6. What is the radius of the triangles inscribed circle?

Jul 29, 2018

In-circle radius color(brown)(r = A_t / s ~~ 0.7416 units.

#### Explanation:

Lengths of sides $a = 2 , b = 7 , c = 6$

In-circle radius $r = {A}_{t} / s$

Semi perimeter of triangle $s = \frac{a + b + c}{2} = \frac{2 + 7 + 6}{2} = 7.5$ units

Area of triangle ${A}_{t} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, using Heron’s formula.

${A}_{t} = \left(7.5 \left(7.5 - 2\right) \left(7.5 - 7\right) \left(7.5 - 6\right)\right) = 5.5621$ sq. units

In-circle radius color(brown)(r = A_t / s = 5.5621 / 7.5 ~~ 0.7416 units.