SOLUTION: A rectangular garden has a perimeter of 140m and an area of 1200m^2. Set up a quadratic equation and solve it algebraically to find the dimensions of the garden.

Question 171365: A rectangular garden has a perimeter of 140m and an area of 1200m^2. Set up a quadratic equation and solve it algebraically to find the dimensions of the garden.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rectangular garden has a perimeter of 140m and an area of 1200m^2. Set up a quadratic equation and solve it algebraically to find the dimensions of the garden.
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Perimeter = 2(L+W)
140 = 2(L+W)
L+W = 70
LW = 1200
---------------
Substitute to get:
W(70-W) = 1200
-W^2 + 70W - 1200 = 0
-------
W = [-70 +- sqrt(70^2-4*-1*-1200)]/(-2)
W = [-70 +- sqrt(100)]/-2
Positive solution:
W = [-70-10]/(-2) = 40 meters (the width)
----
Since L+W = 70, L = 30 meters (the length)
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Cheers,
Stan H.
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