Question

in triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = (x + 3) feet. what is rs? 4 feet 7 feet 10 feet 14 feet

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\), with the longer segment being closer to the vertex. So, \(NS = 2 \times SR\).

Step2: Set up the equation

Given \(NS=(x + 10)\) and \(SR=(x + 3)\), we substitute into the ratio:
\(x + 10=2(x + 3)\)

Step3: Solve for x

Expand the right side: \(x + 10 = 2x+6\)
Subtract \(x\) from both sides: \(10=x + 6\)
Subtract 6 from both sides: \(x = 4\)

Step4: Find RS

Substitute \(x = 4\) into \(SR=(x + 3)\):
\(SR=4 + 3=7\)

Answer:

7 feet