$23 \cdot 32$ The surface area of a rectangular solid is $22 \mathrm{~cm}^{2}$, and the total length of all its edges is $24 \mathrm{~cm}$. Then the length of its diagonal (in $\mathrm{cm}$) is 
(A) $\sqrt{11}$.
(B) $\sqrt{12}$.
(C) $\sqrt{13}$.
(D) $\sqrt{14}$.
(E) cannot be uniquely determined.
(35th American High School Mathematics Examination, 1984)
[Solution] As shown in the figure, $x, y, z$ are the length, width, and height of the rectangular prism, respectively, and $d$ is one of its diagonals. Therefore, we have
$$
\left\{\begin{array}{l}
2 x y+2 x z+2 y z=22, \\
4 x+4 y+4 z=24, \\
d^{2}=x^{2}+y^{2}+z^{2}
\end{array}\right.
$$

From (2), we get $(x+y+z)^{2}=6^{2}$, or
$$
x^{2}+y^{2}+z^{2}+2 x y+2 x z+2 y z=36,
$$

Substituting (1) and (3) into the above equation, we get $d^{2}+22=36$, which means $d=\sqrt{14}$. Therefore, the answer is $(D)$.