A rectangular region R is divided into rectangular areas.

geometry/tiling/rational.sides

Problem

A rectangular region R is divided into rectangular areas.  Show that if
each of the rectangles in the region has at least one side with
rational length then the same can be said of R.

Show solution

"Fourteen proofs of a result about tiling a rectangle" (Stan Wagon)
_The American Mathematical Monthly_, Aug-Sep 1987, Vol 94 #7.  There
was also a fifteenth proof published a few issues later, attributed to
a (University of Kentucky?) student.