Question 1207752: 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?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
Answer by ikleyn(52781)  (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?
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(a) If the pond is a square, then the fence is a square, too,
and the side length of the fenced square is, OBVIOUSLY, 100/4 = 25 feet.
Then the side of the pond itself is 25 - 3 - 3 = 19 feet. ANSWER
(we subtract 3 feet from each side).
(b) Let x be the shorter dimension of the pond, in feet.
Then the longer dimension of the pond is 3x feet.
The dimensions of the fence are (x+6) feet by (3x+6) feet.
The perimeter of the fence is 2(x+6) + 2(3x+6) = 2x + 12 + 6x + 12 = 8x + 24 feet.
We equate it to 100 feet
8x + 24 = 100
and find x: x =  =  = 9.5 feet.
The dimensions of the pond itself are 9.5 feet and 9.5*3 = 28.5 feet. ANSWER
CHECK for the perimeter of the fence 2*(9.5+6) + 2*(28.5+6) = 2*15.5 + 2*34.5 = 31 + 69 = 100 feet. ! correct !
(c) First find the diameter of the fenced circle
D =  =  = 31.831 feet (rounded).
Next, find the diameter of the pond itself
d = 31.831 - 2*3 = 25.831 feet (rounded). ANSWER
(d) The squared pond (a) has the area 19*19 = 361 sq. feet.
The rectangular pond (b) has the area 9.5*28.5 = 270.75 sq. feet.
The circular pond (c) has the area  =  = 524.049 sq. feet.
The greatest area is for circular pond (c). ANSWER
Solved in full, with complete explanations.
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