Answer
The shortest median is $24$ cm in length.
Work Step by Step
The centroid is the point where the medians of a triangle meet. The median portion from the vertex to the centroid is two-thirds of the distance of the median.
This means that the shortest distance from the centroid to each of the vertices belongs to the shortest median. Therefore, we can take the shortest length, $16$ cm, and use it in an equation to find the median:
$16 = \frac{2}{3}(median)$
Divide each side by $\frac{2}{3}$, meaning we multiply by its reciprocal, which is $\frac{3}{2}$:
$median = 16(\frac{3}{2})$
Multiply to simplify:
$median = \frac{48}{2}$
Divide the numerator and denominator by their greatest common factor, $2$:
$median = 24$
