Question

s is the centroid of triangle nql. what is the length of nr? 4 units 8 units 36 units 48 units n 9n - 12 p s 3n q r m l

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1. Here, $\overline{NS} = 9n - 12$ and $\overline{SR}=3n$, and since $\overline{NS} = 2\overline{SR}$, we set up the equation.
$9n - 12=2\times(3n)$

Step2: Solve the equation for n

Expand the right - hand side: $9n - 12 = 6n$.
Subtract $6n$ from both sides: $9n-6n - 12=6n - 6n$, which gives $3n-12 = 0$.
Add 12 to both sides: $3n-12 + 12=0 + 12$, so $3n=12$.
Divide both sides by 3: $n = 4$.

Step3: Find the length of $\overline{NR}$

Since $\overline{NR}=\overline{NS}+\overline{SR}$, and $\overline{NS} = 9n - 12$, $\overline{SR}=3n$.
Substitute $n = 4$ into the expressions. $\overline{NS}=9\times4 - 12=36 - 12 = 24$, $\overline{SR}=3\times4 = 12$.
Then $\overline{NR}=24 + 12=36$.

Answer:

36 units