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Can you make a tetrahedron whose faces all have the same perimeter?

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Ladder and Cube

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Perfectly Square

Age 14 to 16 Challenge Level:

We are first given that: $$x_1 = 2^2 + 3^2 + 6^2$$ $$x_2 = 3^2 + 4^2 + 12^2$$ $$x_3 = 4^2 + 5^2 + 20^2$$ Then show that $x_n$ is always a perfect square.