SOLUTION: A rectangular parking lot is 100ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500ft diagonally. please help thank in advance

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Question 169689This question is from textbook elementary and Intermediate algebra concepts and application
: A rectangular parking lot is 100ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500ft diagonally.
please help thank in advance This question is from textbook elementary and Intermediate algebra concepts and application

Answer by stanbon(75887) (Show Source):
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A rectangular parking lot is 100ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500ft diagonally.
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Let the width be "x" ft.
Then the lengthis "x+100" ft
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Use Pythagoras to solve for "x":
x^2 + (x+100)^2 = 500^2
2x^2 + 200x + 10000 - 500^2 = 0
x^2 + 100x + 5000 - 250*500 = 0
x^2 + 100x - 120000 = 0
x = [-100 +- sqrt(100^2-4*-120000)]/2
Positive solution:
x = 300 ft. (width)
x+100 = 400 ft.(length)
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Cheers,
Stan H.