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

13.5cm

9cm

27cm

18cm

Question

Middle School

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Answer :

luisejr77 luisejr77 · Answer 1 · 2025-03-25T13:15:15-04:00

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]