In triangle ACE, G is the centroid and BE=9. Set up equations to find BG and GE, Then find BG and GE?

NetherCraft 0

1 Answer

  • Where is B located? I will need to assume that B is located at the midpoint of side AC, in order to solve the problem.

    Under this assumption, BE is a median. Along any median, the centroid of a triangle is always located 2/3 of the way from the vertex to the midpoint of the opposite side, so the centroid G is 2/3 of the way from E to B.

    So we have GE = (2/3)BE.

    Furthermore, by segment addition, BG + GE = BE.

    Since BE = 9, GE = (2/3)(9) = 6.

    Then BG + 6 = 9, which gives BG = 3.

    Have a blessed, wonderful day!

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