Let l be the length of the rectangular parking lot and let w be its width.
l = 2w - 9
Area = 315
Area of a rectangle = l x w
Substitute for Area and length in the above
315 = ( 2w - 9) x w
315 = (2w - 9)w
315 = 2w² - 9w
Re-arrange
2w² - 9w - 315 = 0
We can now solve for w using factorisation method
2w² - 30w + 21w - 315 =0
2w ( w - 15) + 21( w - 15) = 0
(w - 15)(2w + 21) = 0
Either w - 15 = 0 or 2w + 21 = 0
w = 15 or w =-10.5
But there is no negative dimension, so we will take only the positive value
substitute w = 15 into l = 2w - 9 to get the length
l = 2(15) - 9 = 30 - 9 = 21
Therefore the dimensions are;
length = 21 yards and width = 15 yards
