Place two bricks adjacent to each other such that one face of the first brick overlaps exactly with a similar face of the second brick. Place the third brick on top of the first brick such that the bottom face of the third brick and the top face of the first brick are similar and overlap each other completely. This creates a vacant position to the side of the third brick and on the top of the second brick in which we can fit an imaginary non-existent identical fourth brick . Since we can locate the vertices of this imaginary identical fourth brick based on the vertices of the original three bricks, the length of the solid diagonal can easily be measured as the distance between two solid-diagonally opposite vertices of this imaginary brick.
I was thinking of an L-shape on the floor, but this is much better from a realistic point of view (Measuring distances with a ruler would be much easier with your method :) )