$23 \cdot 20$ A rectangular solid has a volume of $8 \mathrm{~cm}^{3}$, a total surface area of $32 \mathrm{~cm}^{2}$, and its length, width, and height form a geometric progression. The sum of the lengths of all the edges of this solid (in $\mathrm{cm}$) is
(A) 28 .
(B) 32 .
(C) 36 .
(D) 40 .
(E) 44 .
(36th American High School Mathematics Examination, 1985)
[Solution] Let the length, width, and height of the rectangular prism be $\frac{x}{q}, x, x q$, respectively. According to the problem, we have
$$
\left\{\begin{array}{l}
\frac{x}{q} \cdot x \cdot x q=8, \\
2\left(\frac{x}{q} \cdot x+x \cdot x q+\frac{x}{q} \cdot x q\right)=32,
\end{array}\right.
$$

From (1), we get $x=2$. Substituting $x=2$ into (2) gives $1+q+\frac{1}{q}=4$, and $4\left(\frac{x}{q}+x+x q\right)=4\left(1+q+\frac{1}{q}\right) x=32$. Therefore, the answer is $(B)$.