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D is the centroid of ABC. What is the value of x when BD=2x+40 and BF =18x?​

D is the centroid of ABC. What is the value of x when BD=2x+40 and BF =18x?​-example-1

1 Answer

4 votes

Check the picture below.

let's recall that the centroid of a triangle cuts the medians into a 2:1 ratio, so one part of the median is 2/3 of the whole length whilst the other is 1/3 of it, namely as you see in the picture, thus


BD=\cfrac{2}{3}BF\implies 2x+40=\cfrac{2}{3}18x\implies 2x+40=12x \\\\\\ 40=10x\implies \cfrac{40}{10}=x\implies 4=x

D is the centroid of ABC. What is the value of x when BD=2x+40 and BF =18x?​-example-1
User Tanzeel Kazi
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