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A farmer has 300 feet of fencing and wants to enclose a rectangular area of 3600 square feet What should the dimensions be?
Let's define some variables. We'll call the length L, and the width W. Then we can express the above algebraically:
300 (perimeter) = 2L + 2W
3600 (area) = L x W
Now let's find one variable in terms of the other:
300 = 2L + 2W
300 - 2W = 2L
(300 - 2W)/2 = L
Since we now have the length in terms of width, we can substitute for L in the second equation:
3600 = L x W
3600 = [(300 - 2W)/2] x W
3600 = (300W - 2W2)/2
7200 = 300W - 2W2
---- That was part one of the solution. Now we have to reformat the equation and use the quadratic formula (for the formula and syntax, visit the Wikianswers link below):
-2W2 + 300W - 7,200 = 0
W = [-300+or-(3002 - 4(-2)(-7,200)1/2]/[2(-2)]
W = [-300+or-(90,000 - 57,600)1/2]/-4
W = [-300+or-(32,400)1/2]/-4
W = (-300 + or - 180)/-4
Quadratic equations usually have two answers, since they are parabolas and will most likely cross the x-axis twice.
The first answer is:
w = (-300 + (-180))/-4
W = -480/-4
W = 120
(L = 30)
Or the second answer:
W = (-300 - (-180))/-4
W = (-120)/-4
W = 30
(L = 120)
Either way, the dimensions of the plot must be 120 ft by 30 ft
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Assuming there are two additional width-sized fences to make the division, then 2L + 4W = 1200 ie L + 2W = 600. There are many possible dimensions: L 500, W 50; L 400, W 100 etc etc
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