Let the length and width be l and w, respectively. Then, perimeter = 2(l + w) = 40, and area = lw = 96. In other words: l + w = 20 lw = 96 From here, we could guess and check to get that the length and width are 12 and 8, but let’s do this rigorously: By the first equation, l = 20 - w Substituting into the second equation: (20 - w) * w = 96 w^2 - 20w + 96 = 0 w^2 - 20w + 100 = 4 (w - 10)^2 = 4 w - 10 = 2 or -2 w = 12 or 8 The rest is trivial.