SOLUTION: A farmer decides to enclose a rectangular garden, using ths side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100 ft of fence?

Question 473940: A farmer decides to enclose a rectangular garden, using ths side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100 ft of fence? What should the dimensions of the garden to be to give this area?
The maximum area that the farmer can enclose with 100 ft of fence is ____ sq ft.
The dimensions of the garden to give this area is 50 ft by ___ ft.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Maximum area of a rectangle with fixed perimeter occurs when the rectangle is a square (this can be proven many different ways, either using the vertex of a quadratic, calculus, or AM-GM inequality). The optimal dimensions would therefore be 25 ft * 25 ft, area = 625 sq ft.
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