If a rope $154\text{ m}$ long is divided in the ratio $9:5$, then the length of the shorter piece (in $\text{m}$) is:

Given:
Total length of the rope $=154\text{ m}$
Ratio of division $=9:5$

Let the two pieces be $9x$ and $5x$.
Total length $=9x+5x=14x$

According to the question:

$$14x=154$$

$$x=\frac{154}{14}=11$$

The length of the shorter piece is $5x$:

$$\text{Length of shorter piece}=5\times 11=55\text{ m}$$