Dear Mathsbuddy,Mathsbuddy wrote: Indeed it would be much more interesting, but too complicated for GMat as there are more than 226 similar triangles available! In the attached diagram I have shown a pink alternative similar 45-45-90 triangle in various orientations and 2 sizes. The green triangle introduces the fact that even more orientations of 45-45-90 triangle are possible. There's a challenge for you!
Great work! First of all, you are perfectly correct in your solution to the original question. The similarity question is so complicated it makes my head spin! As you have so elegantly shown, there are a bewildering number of similar triangles in that diagram, at all kinds of funky angles and orientations. My original question could be a challenging GMAT question, but the similarity question is leagues beyond anything the GMAT would expect. That questions gets into the territory of elite competition mathematics.
Great work overall!
Mike
