   Chapter 8.5, Problem 38E 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

Use the results from Exercises 36 and 37 to find the exact length of the radius of the inscribed circle for a triangle with sides of lengths a) 8 , 15 and 17 b) 7 , 9 and 12

To determine

a. To find:

The length of radius of inscribed circle for a triangle with sides of lengths 8, 15 and 17

Explanation

Formula:

Radius of inscribed circle for right angled triangle:

If a, b and c are the lengths of sides of right angled triangle (c is the length of hypotenuse), then the length of radius r of circle inscribed in a right angled triangle is r=aba+b+c.

Radius of inscribed circle for any other triangle:

If a, b and c are the lengths of sides of triangle, then the length of radius r of circle inscribed in a triangle is r=2×s(s-a)(s-b)(s-c)a+b+c

where s is the semi perimeter of the triangle which is given by s=a+b+c2.

Calculation:

First, let’s check whether the triangle is a right angled triangle or not.

From the given lengths of sides of triangle, the longest side measures 17

To determine

b. To find:

The length of radius of inscribed circle for a triangle with sides of lengths 7, 9 and 12

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