posted by Livia on .
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.
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.
240 = 2x+L so L = (240 - 2 x)
A = x L = x (240 - 2 x) = 240 x - 2 x^2
5500 = 240 x - 2 x^2
2750 = 120 x - x^2
x^2 -120 x + 2760 = 0
I get about 89 or 31