SOLUTION: A rectangle has a perimeter of 140 Square feet. Maximize the area of the rectangle

Question 173895: A rectangle has a perimeter of 140 Square feet. Maximize the area of the rectangle
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Perimeter: . Since the perimeter is 140 feet,

Solving for L: ,

Area: , but we know from the perimeter formula that so

Since A(W) is continuous and differentiable the first derivitive set to zero gives the value of the independent variable at a local extrema.

, ,

Since the first derivitive is also differentiable, the sign on the second derivitive at the extreme point will characterize the extreme as a maximum or minimum.

for all in the domain of , so the extreme point is a maximum.

Therefore, a rectangle with perimeter 140 has a maximum area when the width is 35, which means that the length is also 35 and the rectangle is actually a square.
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