Calculate radius of  inscribed circle in triangle A B C with sides 3,4,5?

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to notice that the triangle whose lengths of sides are pythagorean triples `3,4,5` is a right triangle, whose legs measure 3 and 4.

You need to use the following formula that helps you to evaluate the length of radius of the inscribed circle, such that:

`r = S/p`

`S` represents the area of triangle

`p` represents the half-perimeter of triangle

You may evaluate the area of right triangle, such that:

`S = (3*4)/2 => S = 6`

You may also use Heron's formula to evaluate the area, such that:

`S = sqrt(p(p-3)(p-4)(p-5))`

You need to evaluate the half-perimeter, such that:

`p = (3+4+5)/2 => p = 6`

`S = sqrt(6(6-3)(6-4)(6-5)) => S = sqrt(6*3*2*1) => S = sqrt 36 = 6`

Hence, replacing 6 for `S` and `p` yields:

`r = 6/6 => r = 1`

Hence, evaluating the length of radius of the inscribed circle in triangle ABC, under the given conditions, yields `r = 1` .