# The length and width of the garden.

### 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 41E
To determine

Expert Solution

## Answer to Problem 41E

The length of garden is 60 ft and the width of garden is 40 ft.

### Explanation of Solution

Given:

Perimeter of the garden is 200 ft.

Area of the garden is 2400ft2 .

Calculation:

Let the width of garden be x and length of garden be y.

Tabulate the given information into the language of algebra.

 In words In Algebra Width of garden x Length of garden y Perimeter of garden 2(x+y) Area of garden xy

Model the equation for the above information.

Perimeterofgarden=2(l+b)200=2(x+y) (1)

Areaofgarden=l×b2400=x×y (2)

Simplify equation (1) for x,

x+y=2002x+y=100x=100y (3)

Substitute (100y) for x into equation (2),

(100y)y=2400100yy2=2400y2100y+2400=0

Simplify the above equation,

(y60)(y40)=0y=60,y=40

The length of the garden is 60 ft.

Substitute 60 for y in equation (3),

x=10060=40

The width of garden is 40 ft.

Thus, the length of garden is 60 ft and the width of garden is 40 ft.

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