9. (5 points) The side lengths of squares $A, B, C, D$ are $15, b, 10, d$ ($b, d$ are natural numbers), respectively. If their areas satisfy $S_{A}=S_{B}+S_{C}+S_{D}$, then $b+d=$ $\qquad$
【Solution】Solution: According to the analysis, $S_{A}=S_{B}+S_{C}+S_{D}$
$$
\begin{array}{l}
\Rightarrow 15^{2}=b^{2}+10^{2}+d^{2}, \\
\Rightarrow b^{2}+d^{2}=125,
\end{array}
$$
$\because b$ and $d$ are natural numbers, $\therefore$ (1) $b=2, d=11, b+d=13$;
(2) $b=10, d=5, b+d=15$,

Therefore, the answer is: 13 or 15.