They made you find h and r in part (ii) and your final expression had no h's or r's but instead l's. From that, it is obvious that we had to eliminate them. Coincidentally, h, r and l are linked via Pythagoras. After using the pythagoras theorem, we find that the expression we obtain after multiplying out by T's is a quadratic (in terms of T). Only way to make T the subject was to use the quadratic formula. That was my thought process; hope that it explains things clearer