Arectangular parking lot has a length of 7 yards greater than the width. the area of the parking lot is 450 square yards. find the length and the width.

If the width is w and the length is l, then w+7=l and w*l=450. Plugging w+7=l into the second equation, we get (w+7)*w=450 and w^2+7w=450. Subtracting 450 from both sides, we get w^2+7w-450=0. Using the quadratic formula, we get w=(-7+-sqrt(49-4*(-450)*1))/2=(-7+-sqrt(1849))/2=(-7+-43)/2=(-7+43)/2 or (-7-43)/2. Since the width clearly has to be positive, we get (-7+43)/2=36/2=18 as the width. Since the length=w+7=18+7=25, we have our length and width