Enigma 1704: Joe’s triangle
27 June 2012
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From New Scientist #2871, 30th June 2012 [link]
Joe drew a right-angled triangle on an A6 file card. He asked Penny to cut it out and then cut it in two to make two right-angled triangles. Then he asked her to cut each triangle in two to make four right-angled triangles in total. Now Joe’s triangle was very special. Penny found that the lengths of all the sides of all the triangles were a whole number of millimetres.
What was the area of the smallest triangle?
Note: An A6 card has dimensions of 105 mm × 148 mm.