Let width and length be x and y respectively. Perimeter (32in) =2x+2y=> 16=x+y => y=16-x Area, A = xy = x(16-x) = 16x-x^2 The function to maximize is area: A=16 x-x^2 For maximum area, the first derivative of A =0 => A'=16-2x =0 Solving for x: 16-2x=0 =>2x=16 => x=8 in And therefore, y=16-8 = 8 in