Other friendly triangles

Most students are familiar with triangles whose sides are Pythagorean triples like 3-4-5 and 5-12-13.  They may also want to add the 13-14-15 triangle to their list.  It contains both a 5-12-13 triangle and a 3-4-5 triangle (disguised as a 9-12-15, and sharing the altitude of length 12).  This triangle appears often on the AMCs and you’ll save yourself some time if you can recognize it early.

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