SOLUTION: A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long. (a). If the pond is square, what are its dimensions? (b). If the pond is

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Question 146642This question is from textbook New Mexico Edition College Algebra
: A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.
(a). If the pond is square, what are its dimensions?
(b). If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?
(c). If the pond is circular, what is its diameter?
(d). Which pond has the most area? This question is from textbook New Mexico Edition College Algebra

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.
(a). If the pond is square, what are its dimensions?
(b). If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions?
(c). If the pond is circular, what is its diameter?
(d). Which pond has the most area?
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a) 100 feet around a square is 25' per side. 6' is occupied by the deck so the pond is 19 by 19 = 361 square feet.
b) The perimeter is L+6 long by W+6 wide.
2*(L+6) + 2*(W+6) = 100
L = 3W
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2L+12 + 2W+12 = 100
L + W = 38
Sub for L
3W + W = 38
4W = 38
W = 9.5'
L = 3W
L = 28.5'
Area = 270.75 square feet
Note that this is less than the square. A square has the most area of any rectangle of a given perimeter.
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c) The circumference outside the deck is 100', so the diameter is 100/PI.
The diameter of the pond is (100/PI)-6, so the radius is (50/PI)-3
The pond area is
=
= 524.05 square feet
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d) The circle has the most area, it alwasy does for any given perimeter.