Question

20 pts. Involves Triangle Centroids

Answer 1

check the picture below.

so, what does that mean? well, the median GP, gets cut by the point O, at a ratio of 2:1, the same is true for the other medians btw, EN and FM.

that means GO is twice as large as OP.

since we know that OP is 20 -x , let's use that then.


`\bf GO:OP\qquad \cfrac{GO}{OP}\qquad 2:1\qquad \cfrac{2}{1}=\cfrac{GO}{OP}\implies \cfrac{2}{1}=\cfrac{4x-8}{20-x} \\\\\\ 40-2x=4x-8\implies 48=6x\implies \cfrac{48}{6}=x\implies \boxed{8=x}\\\\ -------------------------------\\\\ OP=20-(8)`