   Chapter 8.5, Problem 13E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

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 6 in., 8 in., 10 in. If the length of the radius of the 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 6 in., 8 in., 10 in.

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

Thus perimeter P=6+8+10=24 in.

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

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