Question

In triangle LNP, R is the centroid and LO = 30. Find LR and RO. Enter the answers as numbers.

Answer 1

Answer:

$|LR|=20$

$|RO|=10$

Step-by-step explanation:

The centroid divides the median in the ratio $2:1$.

Thus $|LR|:|RO|=2:1$

This implies that,

$|LO|:|RO|=3:1$

We were given that,

$|LO|=30$

We substitute this value to obtain,

$30:|RO|=3:1$

or

$\frac{30}{|RO|}=\frac{3}{1}$

We cross multiply to get,

$3|RO|=30\times 1$

We divide through by 3, to get,

$|RO|=10$

We can observe from the diagram that

$|LR|+|RO|=|LO|$

$|LR|+10=30$

$|LR|=30-10$

$|LR|=20$