$17 \cdot 113$ The ratio of the three sides of a triangle is $3: 4: 5$, then the ratio of the corresponding heights on these sides is 
(A) $10: 8: 5$.
(B) $20: 15: 12$.
(C) 3:4:5.
(D) $5: 4: 3$.
(Shenyang City, Liaoning Province, China "Yucai Cup" Junior High School Mathematics Competition, 1988)
[Solution 1] Let the three sides be $3x, 4x, 5x$, and the heights be $h_{1}, h_{2}, h_{3}$. Then the area of the triangle $=\frac{1}{2} \cdot 3x \cdot h_{1}=\frac{1}{2} \cdot 4x \cdot h_{2}=\frac{1}{2} \cdot 5x \cdot h_{3}$.
That is, $3h_{1}=4h_{2}=5h_{3}$. Therefore, $h_{2}=\frac{3}{4}h_{1}, h_{3}=\frac{3}{5}h_{1}$.
$$
\therefore \quad h_{1}: h_{2}: h_{3}=h_{1}: \frac{3}{4}h_{1}: \frac{3}{5}h_{1}=1: \frac{3}{4}: \frac{3}{5}=20: 15: 12 \text{. }
$$

Therefore, the answer is $(B)$.
[Solution 2] Let the three sides of the triangle be $3, 4, 5$. From Solution 1, we know $3h_{1}=4h_{2}=5h_{3}$, then $\frac{h_{1}}{4 \cdot 5}=\frac{h_{2}}{3 \cdot 5}=\frac{h_{3}}{3 \cdot 4}$,
i.e., $h_{1}: h_{2}: h_{3}=4 \cdot 5: 3 \cdot 5: 3 \cdot 4=20: 15: 12$.
Therefore, the answer is $(B)$.