The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its height, and inversely as the length of the beam. A beam 12 feet long, with a width of 4 inches and a height of 6 inches can support a maximum load of 800 pounds. If a similar board has a width of 9 inches and a height of 7 inches, how long must it be to support 1200 pounds?
