Enigma 1198: Rightly similar
12 October 2015
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From New Scientist #2354, 3rd August 2002 [link]
George, Fred and Harry have been doodling with pencil and paper — each has drawn a right-angled triangle. The three triangles are similar — that is to say all the same shape but different sizes.
Although they are different sizes, each of the three triangles has one side measuring exactly 10 cm.
None of the other sides are integers. One of the non-integer sides of George’s triangle is the same length as one side of Fred’s, and the other non-integer side of George’s triangle is the same length as one side of Harry’s triangle.
One side of Fred’s triangle has no exact equal in the other two triangles, and the same is true of one side of Harry’s triangle. Of those two sides, Harry’s is the longer.
How much longer?