You have a string that is 24 ft in length. You make a square with part of it and an equilateral triangle with the other part. Keeping these two basic shapes, we decrease the side of the square at the rate of 4 ft/s. At what rate are the sides of the triangle increasing? At what rate is the area of the triangle increasing when the sides of it are 4 ft each? What are the dimensions of the equilateral triangle and square that give the maximum and minimum total areas?