The cover for your topper should have a bit of give in it so you may be able to sew it down the side and it will fit. But before I do that I would try it on the 1/2 of the topper you cut to insure it will fit properly. If not you could still cut it a bit larger and sew down the exposed side. You would then have to make a second one. Now this I have had to do and I took 2 older twin top sheet and sewed two sides, bottom and one longer side. I then placed the topper in the finished sewn sides, measured and sewed the 3rd side to make it like a large pillow case.