# The length of two pieces of wire in inches to nearest tenth. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.6, Problem 88E
To determine

## To find: The length of two pieces of wire in inches to nearest tenth.

Expert Solution

The length of two pieces of wire is 169.1 inches and 190.9 inches.

### Explanation of Solution

Given:

A wire of length 360 inches is cut into two pieces. A square is formed from one piece and a circle is formed from other piece.

Calculation:

Let the side of square be x and radius of circle be r.

Tabulate the given information into the language of algebra.

 In words In algebra Radius of circle r Area of circle πr2 Length of side of square x Area of square x2

Model the equation for the above information.

Areaofcircle=Areaofsquareπr2=x2x=πr

The length of wire is equal to sum of perimeter of circle and perimeter of square.

Perimeterofsqaure+Perimeterofsquare=3604x+2πr=360 (1)

Substitute πr for x in above equation.

4(πr)+2πr=3604×1.77×r+2×3.14×r=3607.08r+6.28r=36013.36r=360

Solve above equation for r.

r=36013.36r=26.95

Substitute 26.95 for r and 3.14 for π into equation (1).

4x+2(3.14)(26.95)=3604x+169.246=3604x=190.8

The length of one wire is 190.8 inches.

The length of other wire is,

length=360190.8=169.2

The length of other wire is 169.2 inches.

Thus, the length of two pieces of wire is 169.1 inches and 190.9 inches.

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