In triangle ABC, AB = 3, AC = 5, and BC = 4. The medians AD, BE, and CF of triangle ABC intersect at the centroid G. Let the projections of G onto BC, AC, and AB be P, Q, and R, respectively. Find GP + GQ + GR.

Answer 1

since the centroid is 2/3 of the way from each vertex to the opposite side, the projections on the sides are 2/3 the length of the sides.

Their sum is thus 2/3 of the perimeter of ABC = 8

Answer 2

8 isn't correct.

Answer 3

You are correct. I calculated using 2/3 of the projection of the median, which is wrong.

I'll think on it some more. You do the same...

Answer 4

It's 16.

Answer 5

16 is correct. Thanks!

Answer 6

no it is not correct

Answer 7

it is not 16

Answer 8

the answer is 47/15

Answer 9

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