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These Triangles

Author: mathforces
Problem has been solved: 14 times

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Lin draws acute-angled triangles with sides $ a $, $ b $ and $ c $, where $ a = y-x $, $ b = x + z $, $ c = y-z $ for some positive integer numbers $ x $, $ y $, $ z $ whose sum does not exceed 10. Find the sum of the values of the perimeters (possibly equal) for all possible (but pairwise distinct) triangles that Lin can draw.





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