1. Given that the total surface area of a rectangular prism is 11, and the sum of its 12 edges is 24, find the length of the diagonal of the rectangular prism.
1. Let the lengths of the three edges meeting at a vertex of a rectangular prism be $a$, $b$, and $c$. From the given conditions and the properties of the diagonal of a rectangular prism, we have
$$
\left\{\begin{array}{l}
2 a b+2 b c+2 c a=11, \\
4(a+b+c)=24 .
\end{array}\right.
$$

From (2), we get $a+b+c=6$.
(3) $)^{2}-$ (1), we get $a^{2}+b^{2}+c^{2}=25$, hence $\sqrt{a^{2}+b^{2}+c^{2}}=5$. Therefore, the length of the diagonal of the rectangular prism is 5.