Im doing my homework and it provides barely any info. here is the question.

Question

Mr Harrison has a very large backyard. He contacted the Clover Pool Company to have a pool installed in the shape of a rectangle. The Clover Pool Company would build a pool that has a perimeter of 72 yards. Mr. Harrison would be allowed to choose the dimensions (length and width) of the pool.He chose the dimensions that would give him a greatest area possible. What are the dimensions of the pool that would give Mr. the greatest area?

Answer 1

If L is the length and W is the width,
2(L+W) = 72
L+W = 36
W = 36 -L
Area = L(36 -L)= 36L- L^2
Set dA/dL = 0 = 0 and solve for L, if you know calculus. If you don't, rewrite the above equation as
Area = 18^2 - (L-18)^2
This is a maximum when the (L-18) term is zero, so L = 18.

Answer 2

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