In triangle RSW, line segment RW is a median and is equal to 27 cm. What is the length of RX? 13.5cm9cm27cm18cm

Accepted Solution

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]