Question 152234: A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
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Let x = width
x+100 = length
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Applying Pythagorean theorem:
x^2 + (x+100)^2 = 500^2
x^2 + x^2 + 200x + 10000 = 250000
2x^2 + 200x - 240000 = 0
x^2 + 100x - 120000 = 0
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Factoring we get:
(x-300)(x+400) = 0
x = {-400, 300}
Only the positive answer makes sense so
x = 300 feet (width)
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x+100 = 400 feet (length)
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Conclusion:
parking lot is 300 feet by 400 feet
