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.
Algebra ->
Quadratic Equations and Parabolas
-> 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.
Log On
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.
----------------
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)
============================================
Cheers,
Stan H.
(