SOLUTION: A rectangular parking lot has a length that is 5 meters more than twice its width. The area of the parking lot is 63 square meters. Find dimensions of parking lot

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Question 727923: A rectangular parking lot has a length that is 5 meters more than twice its width. The area of the parking lot is 63 square meters. Find dimensions of parking lot
Answer by MathLover1(20850) About Me  (Show Source):
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A rectangular parking lot has a length L that is 5m more than twice its width W.
so, we have that L=2W%2B5m...eq. 1
The area A of the parking lot is 63m%5E2.

A=L%2AW...given A=63m%5E2 and L=2W%2B5m, plug it in
63m%5E2=%282W%2B5m%29%2AW....solve for W
63m%5E2=2W%5E2%2B5mW
{{2W^2+5mW-63m^2=0}}}.....use quadratic formula

W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...note that a=2, b=5m, and c=-63m%5E2

W+=+%28-5m+%2B-+sqrt%28+%285m%29%5E2-4%2A2%2A%28-63m%5E2%29+%29%29%2F%282%2A2%29+

W+=+%28-5m+%2B-+sqrt%28+25m%5E2%2B504m%5E2+%29%29%2F4+

W+=+%28-5m+%2B-+sqrt%28+529m%5E2+%29%29%2F4+

W+=+%28-5m+%2B-+23m+%29%2F4+....we need only positive root

W+=+%28-5m+%2B+23m+%29%2F4+

W+=+18m%2F4+

highlight%28W+=4.5m%29+

now find the length

L=2W%2B5m...eq. 1

L=2%2A4.5m%2B5m

L=9m%2B5m

highlight%28L=14m%29