Enigma 1170: Folderol
25 April 2016
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From New Scientist #2326, 19th January 2002 [link]
I have a rectangular piece of paper which I have folded twice and then unfolded again. The first fold was as shown:
In that figure the area of each of the three triangles is a perfect square number of cm², and each area is less than 100 [cm²].
The second fold was through X and parallel to the first. When unfolded the two creases divided the rectangle into three regions, namely two triangles and a pentagon. The area of each was again a perfect square number of cm².
What is the area of the rectangle?