Yeah it's possible, and pretty easy. You just have to create a box to trap the enemy king and keep making it smaller. An example, not best moves.
Hi, there!

You can also check out this link:
http://www.chess.com/article/view/basic-checkmates-king-and-rook-mate

no, black did wrong move in this sample in his first moves.
It doesn't matter, it's a forced checkmate.

I think the OP damn well knows this is mate in X , but in a SebLebian way wants to "entertain" us. Scott gave the general plan and the OP said Scott's first black move is a mistake without further telling why. Worse was , he doubted the knowledge/expertise of the responders. Why then ask ?
Spudnik finished it off by showing the OP is at most a candidate-noob. Case closed I guess.
Mate can be acchieved simply when the loser's King is on any side of the board square, not just in a corner.
It's hard to believe that Anatoly Karpov didn't know it was a win.
Not just hard - impossible.

oh yeah, it most likely I've mistaken when I've maintained about those words belong to Anatoly Karpov. I'm so sorry. But could you be a little lenient with people, when someone made mistakes somehow?

Please, there is no any "entertainment", but, Scottrf, in your first example: what if the black king in one of his last moves will move 12. ... Ka2 instead of Kb1. ?? That move forced stalemate, or we will start the same moves in another corner now...

Please, there is no any "entertainment", but, Scottrf, in your first example: what if the black king in one of his last moves will move 12. ... Ka2 instead of Kb1. ?? That move forced stalemate, or we will start the same moves in another corner now...
If 12 ... Ka2 then 13 Rc2+

It's hard to believe that Anatoly Karpov didn't know it was a win.
Not just hard - impossible.
Possibly it was Boris Karloff?
I'm prepared to believe Boris Karloff thought it might be unwinnable.
Can only one rook with king checkmate to his opponent with only king in the end of game??? I have read from A. Karpoff it's impossible. But some people say this is a wrong thinking. Any authority sourse? The way of situation in the corner sweep aside at once please: that's wrong, it will be only stalemate. In another possibilities you can not force it to the corner, it will be the repeatedely the same moves.