Question

This involves Triangle Centroid. I really do not know how to set this up at all

Answer 1

segment FM is a "median", and therefore, whether or not it bisects the angle at F, it does bisect the EG segment, thus is called a median, it cuts it into two equal halves, therefore, EM = MG.


`\bf EM=MG\implies \cfrac{2x-9}{2}=\cfrac{1+x}{2}\implies 4x-18=2+2x \\\\\\ 2x=20\implies x=\cfrac{20}{2}\implies \boxed{x=10}\\\\ -------------------------------\\\\ EG=EM+MG\implies \cfrac{2(10)-9}{2}+\cfrac{1+(10)}{2}\implies \cfrac{11}{2}+\cfrac{11}{2} \\\\\\ \cfrac{22}{2}\implies 11`