BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.6, Problem 41E
To determine

To find: The length and width of the garden.

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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