Скачать или смотреть Square In A 3-4-5 Triangle Puzzle

What is the area of the square? Thanks to Papa in India for the suggestion!

This puzzle is half of of problem 21 in the 2017 AMC 10A.
https://artofproblemsolving.com/wiki/...

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2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.