1. As shown in Figure $4, \angle B C A$ $=90^{\circ}, C D$ is the altitude. It is known that the three sides of the right triangle $\triangle A B C$ are all integers, and $B D=11^{3}$. Find the ratio of the perimeters of the right triangles $\triangle B C D$ and $\triangle A C D$.
(2002, National Junior High School Mathematics Competition)
(Let $B C=a, C A=b, A B=c$, we know $a^{2}=11^{3} c$. Let $c=11 k^{2}$. Then $a=11^{2} k, b=11 k \cdot$ $\sqrt{k^{2}-11^{2}}$. Let $k^{2}-11^{2}=m^{2}$. Get $k=61, m=$ 60 , the ratio of the perimeters is equal to the similarity ratio, i.e., $\frac{a}{b}=\frac{11}{60}$.)