Question

In triangle RSW, line segment RW is a median and is equal to 27 cm. What is the length of RX?

Answer 1

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 $2:1$.

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:

$\frac{RX}{XW}= \frac{2}{1}$

Solving for "XW":

$XW=\frac{RX}{2}$

Since the lenght of "RX" is 27 centimeters, you know that;

$RX+XW=27$

Substituting $XW=\frac{RX}{2}$ into $RX+XW=27$ and solving for "RX", we get that its lenght is:

$RX+\frac{RX}{2}=27\\\\\frac{3}{2}RX=27\\\\RX=(27)(\frac{2}{3})\\\\RX=18\ cm$