SOLUTION: A rectangle has a perimeter of 71 feet. What length and width should it have so that its area is a maximum?

Question 420953: A rectangle has a perimeter of 71 feet. What length and width should it have so that its area is a maximum?
Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
Denote x ft the length than the width is (71/2)-x and its area is x((71/2)-x).
A(x)=-x^2+35.5x Area function is a downward parabola. The maximum value is the y value of its vertex. x= -b/2a=35.5/2 and y=-(35.5/2)^2+35.5(35.5/2)=315 ft. ( The solution (0,0) is rejected from our real problem)
Answer: The maximum area is approximately 315 square feet.

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