SOLUTION: Could you please help me with an application using a quadratic equation? The question is: The width of a rectangular parking lot is 51 ft less than its length. Determine the d

Question 111414This question is from textbook
: Could you please help me with an application using a quadratic equation?
The question is: The width of a rectangular parking lot is 51 ft less than its length. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
What I've got so far:
x^2+(x-51)^2=250^2
x^2+x^2-102x+2601=62500
2x^2-102x-59899=0
factor out 2
x^2-51x-29949.5=0
I stopped there because I got a decimal number (29949.5) and that seems wrong.
Please help!
Thank you in advance!
Brenda This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Your work so far is good!
Looking at your quadratic equation:, I don't think that you can factor it so you have to use the quadratic formula to solve:

It looks quite formidable with the numbers you have, but it's easy enough with a good calculator.
and you'll get:

Take only the positive answer since lengths cannot be negative.
The length (x) is 200.43 feet.
The width (x-51) is 149.43 feet.
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