SOLUTION: Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find th

Question 139678: Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.

thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
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Draw the picture.
You have three lengths of fence; two are equal so call them "x": one
is not equal but it can be called 120-2x because it is the rest of
the fence after you have used up the two x's.
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EQUATION:
Area of the rectangle = x*(120-2x) = 120x-2x^2
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That is a quadratic with a=-2 and b = 120
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The maximum occurs when x = -b/2a = -120/(2*-2) = 30
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So the two equal sides are each 30 ft.
The other side is 120 - 2x = 120 - 2*30 = 60 ft.
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Cheers,
Stan H.
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