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.