   Chapter 8.5, Problem 15E 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 triangle with sides of lengths 3 in., 4 in., and 5 in., has an area of 6 in2. What is the length of the radius of the inscribed circle?

To determine

To find:

The length of radius of the inscribed circle.

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 3 in., 4 in., 5 in.

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

Thus, perimeter P=3+4+5=12 in.

The area of triangle A is given as 6 in2.

Let the radius of inscribed circle be r in.

Let’s substitute the values of P and A in the formula

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