Asked by martin

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

Triangle N Q L has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, Q M, and L P. The length of line segment N S is x + 10 and the length of line segment S R is x + 3.

What is RS?

4 feet
7 feet
10 feet
14 feet

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 NS = x + 10 and SR = x + 3:
x + 10 = 2(x + 3)
x + 10 = 2x + 6
x = 4

Thus RS = SR = x + 3 = 4 + 3 = 7 feet.