When he "divided his rope in half," it does not follow that he cut it into two parts, each half the original length of the rope. 
No doubt he simply untwisted the strands, and so divided it into two ropes, each of the original length, but one-half the thickness.

He would thus be able to tie the two together and make a rope nearly twice the original length, with which it is quite conceivable that he made good his escape from the dungeon.