This has the great advantage of allowing documents to be easily up and down-scaled on a photocopier - i.e. an A3 document can be printed at 50% scale on an A4 sheet.
I wonder if anyone ever tried to do something similar with imperial units (AKA English units to the US Americans) - i.e. create sheets of papers with side-length of sqrt(2) : 1, and the largest being 1 square yard or similar.