15.5. The area of a trapezoid is three times that of an equilateral triangle. If the heights of the trapezoid and the triangle are both equal to $8 \sqrt{3}$, what is the length of the median of the trapezoid?
15.5. 24
The height of an equilateral triangle is $\frac{\sqrt{3}}{2}$ times the length of each of its sides. Thus, the length of one side of the equilateral triangle is $\frac{2}{\sqrt{3}}(8 \sqrt{3})=16$, and its area is
$$
\frac{1}{2}(8 \sqrt{3})(16)=64 \sqrt{3}
$$

Since the area of the trapezoid is three times that of the equilateral triangle, we have
$$
\begin{array}{c}
\text { (height }) \times(\text { median of the trapezoid })=3 \cdot 64 \sqrt{3} \\
8 \sqrt{3} \times(\text { median of the trapezoid })=3 \cdot 64 \sqrt{3} \\
\text { median of the trapezoid }=24
\end{array}
$$