A rectangular 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