a school is building a rectangular soccer field that as an area of 6000 square yards. the soccer field must be 40 yards longer then its width. determine algebraically the dimensions of the soccer field, in yards.

Let W = width of soccer field

Let L = length

Then, L = W + 40

Area = W x L

Substitute L for W + 40

Then,

6000 = W(W+40)

6000 = W^2 + 40W

W^2 + 40W - 6000 = 0

(W + 100)(W - 60) = 0

W = -100 Throw out because width cannot be negative

W = 60

L = W + 40 = 60 + 40 = 100

Therefore the dimensions of the soccer field are

60 ft width

100 ft length

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