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MathNet 2026 — Part 02 Question 81

Math Olympiad Vault · MathNet 2026 — Part 02

Question 81

Pedrinho has several pieces of wood in the form of a right triangle of legs $1~\mathrm{cm}$ and $2~\mathrm{cm}$. With 4 of these pieces, he manages to assemble a square of side $2~\mathrm{cm}$, as in the figure below. Question illustration Playing with more pieces, he managed to assemble a square using exactly 20 pieces. Assemble you too a square using 20 pieces. (Tip: Calculate the area of the triangles, and thereby calculate the side of the square. Then compare with the hypotenuse of the pieces.)