What is the radius of the circle inscribed in triangle ABC$ if AB = 15, AC = 41, and BC = \(42\)?

Guest Apr 14, 2022

#1**+2 **

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

We can find the semi perimeter by adding all the known sides and dividing by 2.

That would be (15+41+42)/2 = 98/2 = 49

We can find the area of the triangle using the heron's formula:

sqrt(49(49-15)(49-41)(49-42))

= 28*sqrt(119) = approx 305.44393

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

28*sqrt(119)/49

**= (4sqrt(17))/sqrt(7) or approx. 6.23354 units**

If you want, rationalise the radical. Its up to you

**-Vinculum**

Vinculum Apr 14, 2022

#1**+2 **

Best Answer

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

We can find the semi perimeter by adding all the known sides and dividing by 2.

That would be (15+41+42)/2 = 98/2 = 49

We can find the area of the triangle using the heron's formula:

sqrt(49(49-15)(49-41)(49-42))

= 28*sqrt(119) = approx 305.44393

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

28*sqrt(119)/49

**= (4sqrt(17))/sqrt(7) or approx. 6.23354 units**

If you want, rationalise the radical. Its up to you

**-Vinculum**

Vinculum Apr 14, 2022