SOLUTION: A rectangular parking lot has length that is 7 yards less than twice its width. If the area of the land is 130 square yards, what is the dimensions of the land?

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Question 909431: A rectangular parking lot has length that is 7 yards less than twice its width. If the area of the land is 130 square yards, what is the dimensions of the land?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular parking lot has length that is 7 yards less than twice its width. If the area of the land is 130 square yards, what is the dimensions of the land?
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length = 2*width - 7
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Area = length * width
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Equation:
130 = (2w-7)*w
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2w^2 - 7w - 130 = 0
Factor::
(w-10)(2w+13)
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Positive solution:
width = 10 yds
length = 2w-7 = 13 yds
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A rectangular parking lot has length L that is 7yd less than twice its width W.
L=2W-7 ....eq.1
If the area of the land is A=130yd%5E2, then we know that
L%2AW=130yd%5E2 ... plug in L=2W-7
%282W-7%29%2AW=130
2W%5E2-7W=130
2W%5E2-7W-130=0 ...write -7W as 13W-20W
W%5E2%2B13W-20W-130+=+0 ...group
%28W%5E2%2B13W%29-%2820W%2B130%29+=+0
W%28W%2B13%29-10%282W%2B13%29+=+0
%28W-10%29%282W%2B13%29+=+0
solutions:
if W-10+=+0 => W=10
if W%2B13+=+0 => W=-13 => we don't need this solution since the width cannot be negative
so, highlight%28W=10ft%29
now find the length L=2W-7
L=2%2A10-7
L=20-7
highlight%28L=13ft%29
so, the dimensions of the land are: highlight%28L=13ft%29 by highlight%28W=10ft%29