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 36AYU
To determine

To find:

a. If the pond is square, what are its dimensions?

Expert Solution
Check Mark

Answer to Problem 36AYU

a. The dimensions are 19 ft.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

a. The pond is square so its dimensions are

4( x + 6 ) = 100

4x = 76

x = 19

Therefore the dimensions are 19.

To determine

To find:

b. If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?

Expert Solution
Check Mark

Answer to Problem 36AYU

b. Length and width are 9.5 ft , 28.5 ft .

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

b. The pond is rectangular.

So, 2( 3x + 6 ) + 2( x + 6 ) = 100 .

8x = 76

x = 9.5 ft and 28.5 f (three times its width)

Therefore length and width are 9.5 ft , 28.5 ft .

To determine

To find:

c. If the pond is circular, what is its dimensions?

Expert Solution
Check Mark

Answer to Problem 36AYU

c. The dimensions would be 25.85 ft .

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

c. The pond is circular.

C = π . d

That is C = π . ( d + 6 ) .

100 = π . ( d + 6 )

d + 6 = 31.8

d = 25.85

To determine

To find:

d. Which pond has the larger area?

Expert Solution
Check Mark

Answer to Problem 36AYU

d. The area 525 sq.ft.

Explanation of Solution

Given:

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.

Calculation:

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

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