SOLUTION: Toni has 16 feet of edging to make a flower garden.She wants the garden to have the greastest possible area. What dimensions should the garden have?
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Question 147531: Toni has 16 feet of edging to make a flower garden.She wants the garden to have the greastest possible area. What dimensions should the garden have?
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Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Toni has 16 feet of edging to make a flower garden.She wants the garden to have the greastest possible area. What dimensions should the garden have?
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If a circle:
Perimeter = (pi)d = 16
diameter = 16/pi
radius = 8/pi
Area = (pi)(8/pi)^2 = 64/pi sq ft. is approximately 20.3718.. sq ft
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If a rectangle:
P = 2(l + w) = 16
l+w = 8
Area = l*w = (8-w)w = -w^2+8w
Maximum area occurs when w = -b/2a = -8/(-2) = 4
Then l + 4 = 8
And l = 4.
Area = 4*4 = 16 sq. ft.
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Conclusion:
Max area is a circle with perimeter = 16 ft.
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Cheers,
Stan H.
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