# The length, width and height of the box. ### 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 77E
To determine

## To find: The length, width and height of the box.

Expert Solution

The length of the box is 15 ft, width is 2 ft and height is 6 ft.

### Explanation of Solution

Given:

The volume of plywood box is 180ft3 .

The length of box is 9 ft greater than its height and width is 4 ft less than the height.

Formula used: Volume of cuboid

Volume=length×width×height

Calculation:

Let the height of box be x.

Tabulate the given information into the language of algebra.

 In words In algebra Height of box x Length of box x+9 Width of box x−4

Model the equation for the above information.

length×width×height=Volumeofbox(x+9)×(x4)×x=180

Simplify the above equation for x.

(x24x+9x36)x=180(x2+5x36)x=180x3+5x236x180=0

Factor the above polynomial.

x2(x+5)36(x+5)=0(x+5)(x26)=0(x+5)(x+6)(x6)=0x=5,x=6,x=6

Height cannot be negative, so the height of the box is 6 ft.

Length of the box is,

length=x+9=6+9=15

Width of the box is,

width=x4=64=2

Thus, the length of the box is 15 ft, width is 2 ft and height is 6 ft.

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