If your quilt is also big enough for a drop on each side of the mattress, your quilt might be sized a bit bigger. So let's add 10" to each side of the twin mattress size of 39 x 75 for the drop. (I'm making this up - no idea what your quilt size really is!) So your quilt might be 59 x 75. Because the width of the quilt is wider than the usual 42 - 44" quilting fabric, you need to piece the back.
I would purchase at least 85" x 2 = 170" length needed (4.72 yards). Cut the yardage in half (at 85"). Then on one piece, cut 2 strips 9" wide (9" x 85"). Trim selveges. Sew the narrow strips to each side of the 85" full width piece. Now you have a back that is 42" + 9" + 9" = 60" x 85"
A few more ideas:
http://www.allpeoplequilt.com/techni...backs_ss1.html
John Flynn's diagonal pieced back instructions (scroll down the page)
http://www.flynnquilt.com/workshop/FreeLessons/