Final answer:
The length of SW cannot be determined without further information or measurements.
Step-by-step explanation:
In a triangle, the centroid is the point of intersection of the medians, which are the line segments connecting each vertex to the midpoint of the opposite side.
The centroid divides each median into two segments, with the length of the segment closer to the vertex being twice the length of the segment closer to the opposite side.
Therefore, if S is the centroid of triangle XYZ, the length of SW would be twice the length of SM, where M is the midpoint of the side XY.
Without any further information or measurements provided, it is not possible to determine the length of SW.
Typically, if S is the centroid, it divides the medians of the triangle into segments that are in the ratio 2:1, with the larger segment being closer to the vertex. However, without further information such as the lengths of the medians or the sides of the triangle XYZ, we cannot accurately provide the length of SW.