Using straight lines, dissect an isosceles triangle with sides 42, 42, and 21, into six smaller triangles, all similar to the original but with no two of equal sizes.

(In reply to possible solution by broll)

No matter how I twisted and turned this I was never getting there.  Yes, I did start small and try to build as you did but the juggling did not seem to work.  Starting big I always had an isosceles that I had to bisect!!

Following your procedure I missed the last (6th) triangle.  I expected to see its presence earlier than when you posted "hence the upper long side ......".   I did have to carefully reread to ensure that the entity was included. 

While the "(2x),(2x),(x)" relationship was not lost on me, my division of the 42,42,21 triangle into 36 smaller identical isosceles was going to get me nowhere.  But then too, I did disregard size (a la opening paragraph) but the "jigsaw" did not "jiggle"  :-)

I like your description. TU!

Posted by brianjn on 2012-02-15 04:29:49