You have 60 feet of fencing to create a rectangular garden. one side of the garden will be against an existing shed, so that side does not require fencing. determine the dimensions of the garden if the area is 400ft2. determine the dimensions of the garden that yield the maximum area.

the dimensions of the garden that would give max area would be

W (width) = 15 ft and L (length) = 30 ft.

Step-by-step explanation:

Let the length of the garden be L and the width W.

Then L*W must equal 400 ft^2.

The perimeter involving 3 sides is then P = 60 ft = 2W + L, and this can be solved for L:  L = 60 ft - 2W.  Subbing 60 ft - 2W into the previous equation, we get:

(60 ft - 2W)(W) = 400 ft^2, or

-2W^2 + 60W - 400 = 0,

which can be reduced to:

-W^2 + 30W - 200 = 0

We want to find the max area, that is, the max of the function

-W^2 + 30W - 200 = 0

Using the formula x = -b/2a for x-coordinate of vertex, we get:

            30

W = - = 15

          2(-1)

Thus, the dimensions of the garden that would give max area would be

W (width) = 15 ft and L (length) = 30 ft.

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