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2025 SSMO Team Round Problems/Problem 11

Problem

Squares $s_1,$ $s_2,$ and $s_3$ with side lengths $9,$ $17,$ and $10,$ respectively, lie inside of $\triangle ABC$ such that:

  • $s_1$ has a side that lies on $\overline{AB},$ $s_2$ has a side that lies on $\overline{BC},$ and $s_3$ has a side that lies on $\overline{CA}$;
  • each square shares exactly one vertex with each of the other two squares.

Find the perimeter of $\triangle ABC$.

Solution

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