SOLUTION: Jack builds a rectangular animal pen using 20 fence posts placed every 4 feet along the perimeter of the pen.What is the greatest possible area o the animal pen? I tried 20 x

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Question 467046: Jack builds a rectangular animal pen using 20 fence posts placed every 4 feet along the perimeter of the pen.What is the greatest possible area o the animal pen?
I tried 20 x 20 to get 400 which is the answer but that is a square. Since a square is also a rectangle, is that correct?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jack builds a rectangular animal pen using 20 fence posts placed every 4 feet along the perimeter of the pen.What is the greatest possible area o the animal pen?
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Using 20 posts you could get a perimeter of 4*20 = 80 ft.
Perimeter = 2[length + width]
length + width = 40
L = 40-W
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Area = LW
Substitute to get:
A = (40-W)W
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Quadratic form:
Area = 40W-W^2
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Maximum Area occurs when W = -b/(2a) = -40/(-2*1) = 20
Then L = 40-20 = 20
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Max area = 400 sq. ft which gives a square which is also a rectangle.
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Cheers,
Stan H.
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