Question

S is the centroid of triangle NQL. What is the length of NR?

Answer 1

ANSWER

The length of NR is
$36 \: \: units$

EXPLANATION

The centroids divides the medians in the ratio
$2:1$
For instance

$|NS|:|SR|=2:1$

But

$|NS| = 9n - 12$

$|SR|=3n$

We substitute all these values in to the above relation to obtain,

$(9n - 12):3n=2:1$

This can be rewritten as

$\frac{9n - 12}{3n} = \frac{2}{1}$

We cross multiply to obtain,

$1(9n - 12) = 2 \times 3n$

This implies that,

$9n - 12 = 6n$

We group like terms to obtain,

$9n - 6n = 12$

This simplifies to give us,

$3n = 12$

$n = 4$

We can now determine each length as follows,

$|NS| = 9(4 ) - 12$

$|NS| = 36- 12$

$|NS| = 24$

$|SR|=3 \times 4$

$|SR|=12$

From the diagram,

$|NR|=|NS|+|SR|$

$|NR|=24 + 12$

$|NR|=36 \: units$

Answer 2

The answer to this is 36 Units just took the short assignment.

36 Units