Would it be possible to make these slippers I just got the idea for?

OK so. There’s this carpet store in my town that always has a huge cart full of carpet scraps from the sample books they always have on display. Every so often we go in there and get a few pieces to use like rugs when we want a change. So I have this one really nice piece of carpet. I love how it feels. I was think yesterday, could I make take that piece of carpet and draw the outline of my shoes on the back of the carpet and cut that shape out with a box knife, then attach some fabric to the top to make it into slippers? I know I would have to put something (like duct tape?) over the cut edge of the carpet so that it wouldn’t be as sharp and rough.

Does anybody know how to go about doing this? Any tips?