# Math Calculus

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Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let x be the length of two sides perpendicular to the wall as shown. Write an equation of area A of the enclosure as a function of the length x of the rectangular area. Then find the value(s) of x for which the area is 5500 ft^2.

__________________
I I
x I I x
_________________________ Existing Wall

X is the shorter wall. The existing wall is longer than the one across from it, I tried to make it look like that in the picture.

• Math Calculus -

240 = 2x+L so L = (240 - 2 x)
A = x L = x (240 - 2 x) = 240 x - 2 x^2
so
5500 = 240 x - 2 x^2

2750 = 120 x - x^2

x^2 -120 x + 2760 = 0

I get about 89 or 31

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