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HMMT November 2022 U18

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A regular tetrahedron has a square shadow of area 16 when projected onto a flat surface (light is shone perpendicular onto the plane). Compute the sidelength of the regular tetrahedron. (For example, the shadow of a sphere with radius 1 onto a flat surface is a disk of radius 1.)

Dataset text NuminaMath olympiads. Quoted with source.

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4 \sqrt{2}

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