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# Pls help, don't understand.?

A rectangular lot is bordered on one side by a building and the otther 3 sides by 300 m of fencing. Determine the area of the largest lot patio.

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- AshLv 79 months ago
Lets say the fence has length of L and width of W

Then we have L+2W = 300 ( the length along building does not use fence so just one L)

L = 300 - 2W

Area of the lot, A = LW

A = (300-2W)W

A = 300W - 2W²

For optimal area, find derivative and equate to 0

A' = 300 - 4W

0 = 300 - 4W

4W = 300

W = 75 m

so L = 300 - 2(75) = 150 m

Largest Area of lot = 150*75 = 11250 m²

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- ted sLv 79 months ago
2x + y = 300 m and Area = x y = x ( 300 - 2x ) =

- 2 x² + 300 x....maximize this to find x = 75 m

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