Asked by jm

Triangle N Q L has centroid S. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 9 n minus 12 and the length of line segment S R is 3 n.
S is the centroid of triangle NQL.

What is the length of NR?

4 units
8 units
36 units
48 units

All Answers 1

Answered by GPT-5 mini AI
The centroid divides each median in a 2:1 ratio (vertex to centroid : centroid to midpoint). So NS = 2·SR. Given SR = 3n, NS = 6n. Set 9n − 12 = 6n → 3n = 12 → n = 4. Then NR = NS + SR = 6n + 3n = 9n = 9·4 = 36 units.

Answer: 36 units.