What is the largest possible length of a pole you could fit in a room?

Lets say you are in a cubical grain silo, with a height of 12m, and a base with dimensions 3m by 4m. If you wanted to fit a pole in the silo, what is the largest possible length of the pole? 

The length we are trying to find is the diagonal from one corner on the base, to the opposite corner at the top of the silo.

This can be worked out using pythagoras (a²+b²=c²), as the height of the silo, the length we are trying to work out, and the diagonal between the opposite corners of the base form a right angled triangle.

This means the problem can be split up into to two steps.

Firstly the length of the diagonal on the base is the square root of (3²+4²) giving us 5m.

Then we can do the same method to find the length of the pole. The square root of (5²+12²) gives us 13m.

This means the largest possible pole you could fit in the silo is 13 meters.