Question

Triangle X Y Z has centroid S. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments X W, Y V, and Z T. The length of line segment T S is 3 m minus 1, the length of line segment S Z is 4 m + 8, and the length of line segment X S is 2 m + 12.
S is the centroid of triangle XYZ.

What is the length of SW?

5 units
11 units
22 units
28 units

Answer 1

The centroid divides each median in a 2:1 ratio (vertex–centroid : centroid–midpoint = 2:1). So SZ = 2·TS.

Set up: 4m + 8 = 2(3m − 1) → 4m + 8 = 6m − 2 → 2m = 10 → m = 5.

Then XS = 2m + 12 = 2(5) + 12 = 22. Since XS = 2·SW, SW = 22/2 = 11.

Answer: 11 units.