Question 159212
A rectangular patio is surrounded on three sides by a fence (the remaning side is up against the house). If the area of the patio is 38 meter square, and the total length of fence is 18 meters, what is the length and width of the patio.
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A = LW = 38
F = L+2W =18 (F = total fence length)
L = 18-2W
Sub into eqn 1
W*(18-2W) = 38
18W - 2W^2 = 38
W^2 - 9W + 19 = 0
*[invoke solve_quadratic_equation 1,-9,19]
The solver uses x, so sub that for W
W = 4.5 + sqrt(5)/2
W = 4.5 - sqrt(5)/2
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L = 18 - 2W
L = 18 - (9 + sqrt(5))
L = 9 - sqrt(5), W = 4.5 + sqrt(5)/2  Solution 1
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L = 18 - 2W
L = 18 - (9 - sqrt(5))
L = 9 + sqrt(5), W = 4.5 - sqrt(5)/2  Solution 2

The L and W are paired as above.