MATHCOUNTS State Team 2025 (Problem 9)
Solid GeometryHard
Five of the six edges of a tetrahedron each have length inches, and the sixth edge has length inches. What is the volume of the tetrahedron, in cubic inches? Express your answer in simplest radical form.
is the midpoint of . By symmetry, the altitude from to plane lies on line .
The height of the tetrahedron through is the height of through .
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