Create a rectangle with length 3 inches and width 5 inches (which is similar to the figure in question scaled down by 5). The height of the box is represented by the length of the square with side X. By measuring the length of X (multiplied by 5), the volume can be calculated.

By animating the points H, the maximum volume, as well as the size of the square that would produce a volume of 400 cubic inches, can be estimated.

Click above to see there is only 1 maximum value but 2 values of X that produce a volume of 400.