SOLUTION: Susan has 2500 feet of fence and wishes to enclose a rectangular area. Which of the following correctly expresses the area A of the rectangle as a function of the length x of

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Question 42977: Susan has 2500 feet of fence and wishes to enclose a rectangular area. Which of the following correctly expresses the area A of the rectangle as a function of the length x of the rectangle?
a. A(x) = 625x - x^2
b. A(x) = 1000x - x^2
c. A(x) = 1250x - x^2
d. A(x) = 2500x - x^2
e. None of the others

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let, length = x feet and width = y feet.

Length of fence available = Perimeter of the rectangle

So, 2500 = 2(Length + Width)
or 2500 = 2(x + y)
or 2500%2F2+=+%28x+%2B+y%29
or x + y = 1250
or y = 1250 - x

Thus width is (1250 - x) feet.

Now, area is given by
A = Length x Width
or A+=+x%2A%281250+-+x%29
or A+=+1250x+-+x%5E2

Hence, option (c) is correct.