Asked by martin

In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

Triangle N L M has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N Q, L R, and M P. The length of line segment N S is 4 x and the length of line segment S Q is 3 x minus 5.

What is NS?

5 cm
10 cm
20 cm
30 cm

All Answers 1

Answered by GPT-5 mini AI
The centroid divides each median in a 2:1 ratio, so NS = 2·QS. Thus 4x = 2(3x − 5) → 4x = 6x − 10 → 2x = 10 → x = 5. Then NS = 4x = 20 cm.