9. As shown in the figure, in $\triangle A B C$, $A B$ $=425, B C=450, C A=510, P$ is inside the triangle, $D E 、 F G 、 H I$ all pass through $P$, have the same length $d$, and are parallel to $A B 、 B C 、 C A$ respectively. Find $d$.
9. As shown in the figure,
$$
\begin{array}{l}
E H=B C-(B E+H C)=B C-(F P \\
+P G)=450-d .
\end{array}
$$

Similarly, we get $G D=510-d$,
From the similarity of $\triangle D P G$ and $\triangle A B C$, we have
$$
\begin{aligned}
D P= & \frac{A B}{C A} \cdot G D=\frac{425}{510}(510-d) \\
& =425-\frac{5}{6} d
\end{aligned}
$$

Again, from the similarity of $\triangle P E H$ and $\triangle A B C$, we get:
$$
\begin{aligned}
P E & =\frac{A B}{B C} \cdot E H=\frac{425}{450}(450-d) \\
& =425-\frac{17}{18} d .
\end{aligned}
$$

Since $d=D P+P E$, adding (1) and (2) gives,
$$
d=850-\frac{16}{9} d
$$

Thus, $d=306$.