Question

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

Answer 1

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`