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IMO 1985 — Shortlist Question 15

IMO Shortlist · IMO 1985 — Shortlist

Question 15

5a. (FRA 3) Let $K$ and $K'$ be two squares in the same plane, their sides of equal length. Is it possible to decompose $K$ into a finite number of triangles $T_1,T_2,\ldots,T_p$ with mutually disjoint interiors and find translations $t_1,t_2,\ldots,t_p$ such that
$$K'=\bigcup_{i=1}^p t_i(T_i)?$$