As soon as Agent Pathfinder climbed down the ladder (Agent Pathfinder finds a path!!!), her captors sprang out of nowhere and captured her again. She writhed, protested and pleaded, but to no avail. She was taken to a new room as the previous one wasn't "secure" enough. So, they trapped her in a suspended square cage in a triangular room of dimensions 10 metres, 17 metres and 21 metres respectively. The cage was suspended in such a way that two vertices of the cage touched the two shorter walls while one side of the cage touched the room's longest wall. The guards sitting outside the door tried to kill time by calculating the length of the side of the cage. Help them. Also provide a detailed explanation along with your answer.