SOLUTION: Hi, I am trying to understand how you would write out this problem to work it: Thanks for your help, Reuben

Question 146916: Hi, I am trying to understand how you would write out this problem to work it: Thanks for your help, Reuben
Found 2 solutions by Nate, nerdybill:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
width = w
length = 100 + w
c^2 = a^2 + b^2
500^2 = (w)^2 + (100 + w)^2
250,000 = w^2 + 10,000 + 200w + w^2
0 = 2w^2 + 200w - 240,000
0 = w^2 + 100w - 120,000
w = ( -100 +- sqrt( 10,000 + 480,000 ) ) / 2
w = ( -100 +- sqrt( 490,000 ) ) / 2
w = ( -100 +- 700 ) / 2
w = -800 and w = 300
Length can only be positive. w = 300
length = 100 + 300 = 400
300ft by 400ft
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular parking lot is 100 feet longer than it is wide. Determine the dimensions of the parking lot if it measures 500 feet diagonally.
.
Let w = width of lot
then w+100 = length of lot
.
apply Pythagorean theorem:
w^2 + (w+100)^2 = 500^2
expanding:
w^2 + w^2 + 200w + 10000 = 250000
2w^2 + 200w + 10000 = 250000
2w^2 + 200w - 240000 = 0
w^2 + 100w - 120000 = 0
(w - 300)(w + 400) = 0
w = {300, -400}
Can't be negative so
w = 300 ft (width)
w+100 = 400 ft (length)

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