Find the length of the diagonal of a rectangle whose length is 7 feet greater than its width and whose total area is 120 square feet.

Let width be w then the length l = w + 7

Area = w(w + 7) = 120
w^2 + 7w - 120 = 0
w = 8 or -15  (ignore negative)

So w = 8 and l = 8+7 = 15

Length of the diagonal d is calculated using Pythagoras theorem:-

d^2 = 8^2 + 15^2 =  289

diagonal = sqrt 289  = 17 feet (answer)