SOLUTION: A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

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Question 148764: A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

Answer by nerdybill(7384) (Show Source):
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A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
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Let w = width of parking lot
then
w+50 = length of parking lot
.
Using Pythagorean theorem:
w^2 + (w+50)^2 = 250^2
w^2 + (w^2 + 100w + 2500) = 62500
2w^2 + 100w + 2500 = 62500
2w^2 + 100w - 60000 = 0
w^2 + 50w - 30000 = 0
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If it is too difficult factor, use the "quadratic equation".
You'll get two solutions:
150, -200
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since it can't negative:
width=150 ft
length = 200 ft
.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=122500 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 150, -200. Here's your graph: