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Contrived Tetrahedron

Source: 2015 AMC 12A #16 / 10A #21

February 4, 2015
geometry3D geometrytetrahedronanalytic geometrycalculusvector

Problem Statement

Tetrahedron ABCDABCD has AB=5AB=5, AC=3AC=3, BC=4BC=4, BD=4BD=4, AD=3AD=3, and CD=1252CD=\tfrac{12}5\sqrt2. What is the volume of the tetrahedron?
<spanclass=′latex−bold′>(A)</span>32<spanclass=′latex−bold′>(B)</span>25<spanclass=′latex−bold′>(C)</span>245<spanclass=′latex−bold′>(D)</span>33<spanclass=′latex−bold′>(E)</span>2452<span class='latex-bold'>(A) </span>3\sqrt2\qquad<span class='latex-bold'>(B) </span>2\sqrt5\qquad<span class='latex-bold'>(C) </span>\dfrac{24}5\qquad<span class='latex-bold'>(D) </span>3\sqrt3\qquad<span class='latex-bold'>(E) </span>\dfrac{24}5\sqrt2
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