Since we know that the perimeter is 32 meters, 2W + 120/W = 32 (meters)
Multiplying all terms by W: 2W^2 + 120 = 32W, or
w^2 + 60 = 16w, or w^2 - 16w + 60 = 0.
Using the Quadratic Formula to find w:
-(-16) plus or minus sqrt(20) w = ----------------------------------------- 2 16 plus or minus 2sqrt(5) = ------------------------------------ 2
= 8 plus or minus sqrt(5). This produces 2 positive solutions. Since w represents width, discard any negative result. You may have to check twice, since you will have 2 different widths.