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

Question

2769 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-29T14:45:49

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

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

In-circle radius #r = A_t / s#

Semi perimeter of triangle #s = (a + b + c)/2 = (2+7+6)/2 = 7.5# units

Area of triangle #A_t = sqrt(s (s-a) (s-b) (s-c))#, using Heron’s formula.

#A_t = (7.5 (7.5-2) (7.5-7) (7.5-6)) = 5.5621# sq. units

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