SOLUTION: A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 270 square yards. Find the length and width.

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 270 square yards. Find the length and width.      Log On

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Question 163870: A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 270 square yards. Find the length and width.
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
The length is 3 yards greater than the width.
L=3%2BW
The area of a rectangle is
A=L%2AW=270
%283%2BW%29W=270
W%5E2%2B3W=270
W%5E2%2B3W-270=0
Use the quadratic formula,
W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
W+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-270%29+%29%29%2F%282%2A1%29+
W+=+%28-3+%2B-+sqrt%28+9%2B1080+%29%29%2F%282%29+
W+=+%28-3+%2B-+sqrt%281089+%29%29%2F%282%29+
W+=+%28-3+%2B-+33%29%2F%282%29+
W%5B1%5D=%28-3%2B33%29%2F2=30%2F2=15
W%5B2%5D=%28-3-33%29%2F2=-36%2F2=-18
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A negative width doesn't make sense for our problem, so we'll only use the positive solution.
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From above,
L=3%2BW
L=3%2B15
L=18
The lot is 15 yards wide, 18 yards long.