Question

What is the radius of the circle inscribed in triangle $abc$ if $ab = 15, ac = 41, bc = 52$?

Answer 1

It would be 13/3
What is this question from anyway?
Seems familiar.

Answer 2

4.33 unit ( approx )

Explanation:

The radius of the circle inscribed in triangle is,

`r=(A)/(S)`

Where,

A = Area of the triangle,

S = Semi perimeter of the triangle,

Given,

In triangle ABC,

AB = 15, AC = 41, BC = 52

`S=(AB+AC+BC)/(2)=(15+41+52)/(2)=(108)/(2)=54`

By the Heron's formula,

Area of the triangle ABC,

`A=√(S(S-15)(S-41)(S-52))`

`=√(54(54-15)(54-41)(54-52))`

`=√(54* 39* 13* 2)`

`=√(54756)`

`=234\text{ square unit}`

Hence, the radius of the circle inscribed in triangle ABC,

`r=(234)/(54)\approx 4.33\text{ unit}`