It depends on the width of the backing, how much piecing you are willing to do, and how much you need around the edges. A longarmer usually wants 3-4" all the way around, so the back would need to be 106-108 x 118-20. If you're quilting yourself you may be happy with 2-3 inches instead. For the standard 45" fabric I would buy 10 yards and then make two lengthwise seams.
Actually I would *use* 10 yards, but would purchase a bit more, perhaps 10 1/2.