SOLUTION: 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 h
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Question 252964: 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 the greatest area possible.
What are the demensions of the pool that would give Mr. Harrison the greatest area? Answer by Greenfinch(383) (Show Source):
You can put this solution on YOUR website! If the length of one side is X, the other side is 36 - X, so that 2X + (72 -2x) = 72.
The Area is X(36 -X)= 36X + X^2
For that to be greatest requires dy/dx to be 0
ie 36 - 2X = 0
x = 18
The largest area is for a square pool 18 yards on each side.
