Answer: LAST OPTION.
Step-by-step explanation:
By definition the line segment that goes from a vertex of the triangle to the midpoint of the oposite side, is called "Median of a triangle".
The medians of a triangle intersect at point called "The centroid of the triangle" and this divides each median in a ratio [tex]2:1[/tex].
In this case, you can notice that the Centroid of the given triangle is the point "X".
Based on the explained before, we can write the following porportion:
[tex]\frac{RX}{XW}= \frac{2}{1}[/tex]
Solving for "XW":
[tex]XW=\frac{RX}{2}[/tex]
Since the lenght of "RX" is 27 centimeters, you know that;
[tex]RX+XW=27[/tex]
Substituting [tex]XW=\frac{RX}{2}[/tex] into [tex]RX+XW=27[/tex] and solving for "RX", we get that its lenght is:
[tex]RX+\frac{RX}{2}=27\\\\\frac{3}{2}RX=27\\\\RX=(27)(\frac{2}{3})\\\\RX=18\ cm[/tex]
