Question 80787: A rectangular parking lot is 50 ft longer than it is wide. Determne the dimensions of the parking lot if it measures 250 ft. diagonally.
Answer by dolly(163)   (Show Source):
You can put this solution on YOUR website! Let the width of the parking lot be 'x' ft
So length = (x+50) ft
Given the diagonal measures = 250 ft
The width, length and the diagonal together form a right triangle.
Applying Pythagorean theorem,
x^2 + (x+50)^2 = (250)^2
==> x^2 + x^2 + 100x + 2500 = 62500
==> 2x^2 + 100x + 2500 - 62500 = 0
==> 2x^2 + 100x - 60000 = 0
==> x^2 + 50x - 30000 = 0 [dividing by 2]
==> x^2 + 200x - 150x - 30000 = 0
==> x(x+200) - 150(x + 200) = 0
==> (x+200) (x-150) = 0
==> x+200 = 0 or x-150 = 0
As x denotes width, x cannot be negative.
Thus we take x = 150 only
So the length of the parking lot = x+50 = 200 ft
Width of the parking lot = x = 150 ft.
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