Prince Atif built a T-shaped bridge using 2 bridges and crossed the moat (Prince of Parzania - Rescuing the Damsel-in-Distress). On reaching the other side of the moat, he realised that the castle was enormous. The entrance to the castle, however, was locked. He suddenly saw a ladder that was balanced against a box (as shown). The top end of the ladder rested against an open window that would help the prince gain entry into the castle. He was sure that was the route taken by Jaffer to visit the princess from time to time. The dimensions of the box were 64m and 27m. The only position in which the ladder could touch the castle wall, the box and the ground is the one depicted here. Using this information, deduce the length of the ladder. Provide a detailed explanation along with your answer.