Question

s is the centroid of triangle nql. what is the length of nr? 4 units 8 units 36 units 48 units

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\), so the length from the vertex to the centroid is twice the length from the centroid to the midpoint. Thus, \(NS = 2 \times SR\), so \(9n - 12 = 2(3n)\).

Step2: Solve for \(n\)

Simplify the equation: \(9n - 12 = 6n\). Subtract \(6n\) from both sides: \(3n - 12 = 0\). Add 12 to both sides: \(3n = 12\). Divide by 3: \(n = 4\).

Step3: Find \(SR\) and \(NS\)

Substitute \(n = 4\) into \(SR = 3n\), so \(SR = 3(4) = 12\). \(NS = 9(4) - 12 = 36 - 12 = 24\).

Step4: Find \(NR\)

\(NR = NS + SR = 24 + 12 = 36\) units.

Answer:

36 units