Question 33263
Total length of the fence = Sum of three sides of the garden;
Sum of three sides of the garden =length+width+width;
If length of the fence = x ft, the width of the fence would be = (32-x)/2;
The area of the fenced portion = Length*WIdth = x(32-x)/2; 
If A(x) is the function for area, A(x) = x(32-x)/2 = -x^2/2 + 16x;
A(x) is a parabola, opening downward; the maximum value is attained at its vertex; x-coordinate of Vertex of A(x) = -b/2a = 16/1 = 16;
So, the length and width of the fence to maximize the area is 16 ft and 8 ft respectively.