Question 1033413: Stacy has 30 meters of fencing that she wishes to use to enclose a rectangular garden. If all of the fencing is used, what is the maximum area of the garden, in square meters, that can be enclosed?
A)48.75
B)56.25
C)60.50
D)168.75
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The maximum area for a rectangle is when it is a square. This can be proven a variety of ways, but I will use that.
7.5 m on a side
7.5^2=56.25 sq m. B
Let x equal a side of a rectangle and y equal the other side
P=2x+2y
(P-2y)/2=x
area ix xy=y(P-2y)/2=[Py-2y^2]/2
The maximum of this quadratic (which has a vertex at highest point, because the y^2 coefficient is negative is at (1/2)(P-4y).
Set that equal to 0, multiply by 2 and move terms, and 4y must equal P.
y=(1/4)P, and that is a square.
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