Solution: The area of the triangle is $ \frac12 \times 9 \times 12 = 54 $ km². The altitudes corresponding to each side are $ \frac2 \times 549 = 12 $, $ \frac2 \times 5412 = 9 $, and $ \frac2 \times 5415 = 7.2 $. The shortest altitude is $ 7.2 $ km, or $ \frac365 $. Thus, the length is $\boxed\dfrac365$ km. - Crosslake