Space diagonals of a cuboid

You have three congruent cuboids, and a ruler. How can you find the length of the cuboid's diagonal without using a formula, such as the Pythagorean theorem?

The distance between A and B, in the figure below, is the length of the cuboid's diagonal.

What other internal diagonals of polyhedrons can be measured by some fixed number of congruent copies? Certainly the internal diagonal of a parallelpiped, or any internal diagonal of any prism, such as a penatagonal prism. What about, say, the longest internal diagonal of an octahedron? What about any of the interal diagonals of icosahedrons?

This puzzle was taken from "The Inquisitive Problem Solver." The questions following the solution are my own.