SOLUTION: A rectangle has 200 feet of fencing with which to enclose two adjacent rectangle corrals. What dimensions should be used so the enclosed area will be a maximum? what is the maximum

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Question 439747: A rectangle has 200 feet of fencing with which to enclose two adjacent rectangle corrals. What dimensions should be used so the enclosed area will be a maximum? what is the maximum area?
Answer by stanbon(75887) About Me  (Show Source):
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A rectangle has 200 feet of fencing with which to enclose two adjacent rectangle corrals. What dimensions should be used so the enclosed area will be a maximum? what is the maximum area?
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Draw the picture of 2 adjacent rectangles.
Let height be "h" (Note: there are 3 of them)
Then width = (1/2)(200-3h)
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Area = (h/2)(200-3h)
Area = 100h - (3/2)h^2
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Max area occurs when
h = -b/(2a)
= -100/(2(-3/2))
= 100/3 ft.
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Then length = (1/2)(200-(3/2)(100/3))
= (1/2)(50)
= 25 ft.
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Max area = 25*(100/3) = 833 1/3 sq. ft.
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Cheers,
Stan H.