   Chapter 8.5, Problem 39E 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) 7 , 24 and 25 b) 9 , 10 and 17

To determine

(a)

To find:

The length of radius of inscribed circle for a triangle.

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 25.

252=625.

The sum of squares of remaining two sides =72+242=49+576=625

To determine

(b)

To find:

The length of radius of inscribed circle for a triangle.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Expand each expression in Exercises 122. x(4x+6)

Finite Mathematics and Applied Calculus (MindTap Course List)

Draw a polygon for the distribution of scores shown in the following table. X f 6 2 5 5 4 3 3 2 2 1

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Proof Prove the difference, product, and quotient properties in Theorem 2.15.

Calculus: Early Transcendental Functions (MindTap Course List)

The slope of the tangent line to y = x3 at x = 2 is: 18 12 6 0

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 