Question 146916
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)