Question

Please help and show workings

Answer 1

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,

$QC:FQ=2:1$

Let the length of QC and FQ are 2x and x respectively.

We have, FQ=9.

$x=9$

Now,

$QC=2x$

$QC=2(9)$

$QC=18$

And,

$FC=FQ+QC$

$FC=9+18$

$FC=27$

Therefore, the length of FC is 27 units and length of QC is 18 units.