In △RST, RW=27 cm .What is the length of RX¯¯¯¯¯¯?Enter your answer in the box.

Accepted Solution

Answer:[tex]RX=18\ cm[/tex]Step-by-step explanation:see the attached figure to better understand the problemwe know thatA centroid of a triangle is the point where the three medians of the triangle intersect. The centroid divides each median in a ratio of [tex]2:1[/tex]In this problem the point X is the centroid of the triangle RSTso[tex]\frac{RX}{XW} =\frac{2}{1}[/tex][tex]RX=2XW[/tex] ----> equation A[tex]RW=RX+XW[/tex]solve for RX[tex]RX=RW-XW[/tex] -----> equation Bequate equation A and equation B[tex]2XW=RW-XW[/tex][tex]3XW=RW[/tex][tex]XW=RW/3[/tex]we have[tex]RW=27\ cm[/tex]substitute[tex]XW=27/3=9\ cm[/tex]Substitute in equation A[tex]RX=2XW[/tex][tex]RX=2(9)=18\ cm[/tex]