Consider a rectangular piece of paper ABCD with AB ≠ AD

Show how you can fold this piece of paper into five pieces of equal area.

*** Using any given instrument like straightedge, compass, protractor, ruler etc. is NOT permissible.

(In reply to re(3): a solution by Steve Herman)

I think we are dealing with papers of differing aspect ratios.  I'm using 8.5x11 with CE=2.125

When I attempt your approach the perpendicular bisector doesn't pass through BC.

But even if one of the points cannot be folded up it doesn't really matter.  You only need one of E', F', G' or H' and the rest can be created by halving/doubling.

If this doesn't make sense I'll try constructing with geometer's sketchpad so I can stretch things and really see what is possible.

Posted by Jer on 2014-04-27 01:00:39