   Chapter 8.CT, Problem 16CT ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# The area of a right triangle whose sides have lengths 5 in., 12 in,. and 13 in. is exactly 30 in2. Use the formula A = 1 2 r P to find the length of the radius of the circle that can be inscribed in this triangle.                                 _

To determine

To find:

The length of the radius of the circle that can be inscribed in the triangle.

Explanation

Given:

The area of a right triangle whose sides have lengths 5 in, 12 in, and 13 in is exactly 30 in2.

Theorem:

The area A of a triangle whose perimeter is P and has the length of the radius r of its inscribed circle is given by A=12rP.

From the given, let a=5 in, b=12 in, c=13 in, and A=30 in2.

The perimeter is, P=a+b+c=5+12+13=30 in

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