Question 935035: A rectangular lot is to be enclosed with 500 feet of fencing. The area of the lot is 14,400 square feet. Find the dimensions of the rectangular lot.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 2L + 2w = 500
Lw = 14400
w = 14400/L
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2L + 2w = 500
2L + 2(14400/L) = 500
2L + 28800/L - 500 = 0
2LL - 500L + 28800 = 0
LL - 250L + 14400 = 0
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the above quadratic equation is in standard form, with a=1, b=-250 and c=14400
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -250 14400
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the quadratic has two real roots at:
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L = 160
L = 90
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the larger root makes better sense as a length rather than a width:
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L = 160
w = 14400/L
w = 14400/160
w = 90
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answer:
L = 160 ft
w = 90 ft
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