ANSWER
The length of NR is
[tex]36 \: \: units[/tex]
EXPLANATION
The centroids divides the medians in the ratio
[tex]2:1[/tex]
For instance
[tex]|NS|:|SR|=2:1[/tex]
But
[tex]|NS| = 9n - 12[/tex]
[tex]|SR|=3n[/tex]
We substitute all these values in to the above relation to obtain,
[tex](9n - 12):3n=2:1[/tex]
This can be rewritten as
[tex] \frac{9n - 12}{3n} = \frac{2}{1} [/tex]
We cross multiply to obtain,
[tex]1(9n - 12) = 2 \times 3n[/tex]
This implies that,
[tex]9n - 12 = 6n[/tex]
We group like terms to obtain,
[tex]9n - 6n = 12[/tex]
This simplifies to give us,
[tex]3n = 12[/tex]
[tex]n = 4[/tex]
We can now determine each length as follows,
[tex]|NS| = 9(4 ) - 12[/tex]
[tex]|NS| = 36- 12[/tex]
[tex]|NS| = 24[/tex]
[tex]|SR|=3 \times 4[/tex]
[tex]|SR|=12[/tex]
From the diagram,
[tex]
|NR|=|NS|+|SR|[/tex]
[tex]
|NR|=24 + 12[/tex]
[tex]|NR|=36 \: units[/tex]
