Given:
In triangle ABC, Q is the centroid and FQ=9.
To find:
The length of FC and QC.
Solution:
We know that, centroid is the intersection point of medians of a triangle and medians divide teach other in 2:1. So, centroid divided each median in 2:1.
CF is a median and Q is the centroid. So,
[tex]QC:FQ=2:1[/tex]
Let the length of QC and FQ are 2x and x respectively.
We have, FQ=9.
[tex]x=9[/tex]
Now,
[tex]QC=2x[/tex]
[tex]QC=2(9)[/tex]
[tex]QC=18[/tex]
And,
[tex]FC=FQ+QC[/tex]
[tex]FC=9+18[/tex]
[tex]FC=27[/tex]
Therefore, the length of FC is 27 units and length of QC is 18 units.
