There is a cuboid with sides of 3 centimetres, 4 centimetres and 12 centimetres - what is the length of the long diagonal between opposite corners?
Taking the face which is 3 centimetres by 4 centimetres, use Pythagoras and the diagonal of this face is 5 centimetres - 5 squared equals 4 squared plus 3 squared.
There is now a triangle with two sides of 12 centimetres and 5 centimetres and the hypotenuse is the long diagonal. Again using Pythagoras the long diagonal is 13 centimetres - 13 squared equals 5 squared plus 12 squared.