Question

In △RST, RW=27 cm .

What is the length of RX¯¯¯¯¯¯?

Enter your answer in the box.

Answer 1

`RX=18\ cm`

Explanation:

see the attached figure to better understand the problem

we know that

A centroid of a triangle is the point where the three medians of the triangle intersect. The centroid divides each median in a ratio of
`2:1`

In this problem the point X is the centroid of the triangle RST

so

`(RX)/(XW) =(2)/(1)`

`RX=2XW` ----> equation A

`RW=RX+XW`

solve for RX

`RX=RW-XW` -----> equation B

equate equation A and equation B

`2XW=RW-XW`

`3XW=RW`

`XW=RW/3`

we have

`RW=27\ cm`

substitute

`XW=27/3=9\ cm`

Substitute in equation A

`RX=2XW`

`RX=2(9)=18\ cm`