Ken's Puzzle of the Week

Triangle and Rectangle Pairs

A triangle and rectangle have the same area and perimeter.  All sides are integers.

  1. Find such a pair with the smallest area?  And the next smallest?
  2. Can you find such a pair with a right triangle?
Source: Original.  For the second question, a good table of Pythagorean Triples is: http://grail.cba.csuohio.edu/~somos/rtritab.txt.
Solution
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