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Question
find the length and width of a rectangle that has the area of 64 square feet and a minium perimeter?
I can figure out the equations having a hard time finding critical numbers.
Thanks
The perimeter is given by P = 2W + 2L, where W is the width, and L is the length.
The area is given by A = WL. It is known that the area is 64, so 64 = WL.
Solve this equation for W, as in W = 64/L.
The perimeter equation is now P = 2(64/L) + 2L = 128(L^-1) + 2L.
Find dP/dL, set it to 0, solve for L, and that gives you the solution for L.
Note that dP/dL = -128/Lē+ 2. Using W = 64/L, W can be found.
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Scotto
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