Question

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

Answer 1

`|LR|=20`

`|RO|=10`

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

`(30)/(|RO|)=(3)/(1)`

We cross multiply to get,

`3|RO|=30* 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`