SOLUTION: You have 180 yards of fencing to use on three sides of a garden. The fourth side is the tool shed. a. What is the maximum area that you can fence? b. What are the dimensions of

Question 869209: You have 180 yards of fencing to use on three sides of a garden. The fourth side is the tool shed.
a. What is the maximum area that you can fence?
b. What are the dimensions of the garden?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the dimensions of the area be x-y-x where y is the length parallel to the tool shed.
The area of the rectangle is
The amount of fencing used is
Substitute into A,

To maximize A, find the derivative of area with respect to x.

Then

So,
a.
b.,
.
.
.
If you had made a semi-circle with the fencing, then

and the area would have been
}

a 27% increase in garden area using the same amount of fence.

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