A rectangular garden with an area of 250 square meters is to be located next to a building and fenced on three sides, with the building acting as a fence on the fourth side. Find the dimensions of the garden that will minimize the amount of fencing required.
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Answer:
Let the length be x and width be y
Area = length × width
xy = 250
y = 250/x.
Now,
Perimeter = 2(length + width)
⇒ 2(x + y)
⇒ 2(x + 250/x)
⇒ 2x + 500/x
Find the derivative of this. I hope you can find it! :)
Equating it to "0" (Optimization)
Or
Now, y = 250/x.
Therefore, x should be 5√10; y should be 5√10.
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