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Question
Point G is the centroid of ABC.
If l(RG) = 2.5 then l(GC) = ______.
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Solution
If l(RG) = 2.5 then l(GC) = 5.
Explanation:
In ∆ABC, the medians AP, BQ, and CR to the sides BC, CA, and AB respectively intersect at G. Since then the centroid of a triangle divides the medians in the ratio of 2 : 1, then AG : GP = BG : GQ = CG : GR = 2 : 1
We have, CG: GR = 2 : 1
⇒ `(GC)/(RG) = 2/1`
⇒ `(GC)/(2.5) = 2/1`
⇒ GC = `(2 xx 2.5)/1`
⇒ GC = `5.0/1`
⇒ GC = 5
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