24) It is well known that the area of an equilateral triangle with a unit side cannot be expressed as a rational number (i.e., as a ratio of integers). Are there tetrahedra that have such a triangle as their base and whose volume can be expressed as a rational number?

$\begin{array}{ll}\text { (A) None exist (B) infinitely many exist } & \text { (C) only the regular tetrahedron }\end{array}$

(D) only tetrahedra with height equal to $6 \sqrt{3}$ (E) only if the tetrahedron is right.
24) The answer is (B). The base area is $\frac{\sqrt{3}}{4}$, and thus all tetrahedra with height $q \sqrt{3}$, where $q$ is a rational number, have a volume that can be expressed as a rational number.