Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter A.8, Problem 35AYU
To determine

To find:

a. If the length of the garden is to be twice its width, what will be the dimensions of the garden?

Expert Solution
Check Mark

Answer to Problem 35AYU

a. The dimensions are 10 ft by 5 ft.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

a. Length of the garden is to be twice its width.

So, 2( w + 4 ) + 2( 2w + 4 ) = 46 .

6w = 30

w = 5

Therefore width is 5 and length is 10.

To determine

To find:

b. What will be the area of the garden?

Expert Solution
Check Mark

Answer to Problem 35AYU

b. The area is 50 sq.ft.

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

b. The area = (width)(length) = 5( 10 ) = 50 sq.ft .

To determine

To find:

c. If the length and width of then garden are to be the same, what will be the dimensions of the garden?

Expert Solution
Check Mark

Answer to Problem 35AYU

c. The dimensions would be 7.5 ft by 7.5 ft .

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

c. The dimensions of the garden length and width are same.

2( w + 4 ) + 2( w + 4 ) = 46

4w = 30

w = 7.5 ft

Therefore, the dimensions would be 7.5 ft by 7.5 ft .

To determine

To find:

d. What will be the area of the square garden?

Expert Solution
Check Mark

Answer to Problem 35AYU

d. The area would be 56.25 sq.ft .

Explanation of Solution

Given:

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.

Calculation:

d. The area of square is =  ( 7.5 ) 2  = 56.25 sq.ft .

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