Chapter 8.5, Problem 14E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# A circle is inscribed in a triangle having sides of lengths 5 in., 12 in., and 13 in. If the length of the radius of inscribed circle is 2 in., find the area of the triangle.

To determine

To find:

The area of triangle.

Explanation

Formula:

Area of a triangle with an inscribed circle:

If P is the perimeter of the triangle and r is the length of radius of its inscribed circle, then the area A of the triangle is given by

A=12rP

Calculation:

The lengths of sides of triangle is given as 5 in., 12 in., 13 in.

Perimeter of triangle is sum of lengths of all sides of triangle.

Thus perimeter P=5+12+13=30 in.

The radius of inscribed circle (r) is given as 2 in

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