Given:
The figure of a triangle LMN.
P is the centroid of triangle LMN.
To find:
14. Find the value of PN if QN=30.
15. Find the value of PN if QN=9.
Solution:
We know that the centroid in the intersection of medians of a triangle and centroid divides each median in 2:1.
Since P is the centroid it means NQ is the median from vertex N. It means P divides the median NQ in 2:1. So, PN:PQ=2:1.
14. We have QN=30.
[tex]PN=\dfrac{2}{2+1}QN[/tex]
[tex]PN=\dfrac{2}{3}(30)[/tex]
[tex]PN=2(10)[/tex]
[tex]PN=20[/tex]
Therefore, the value of PN is 20 when QN=30.
15. We have QN=9.
[tex]PN=\dfrac{2}{2+1}QN[/tex]
[tex]PN=\dfrac{2}{3}(9)[/tex]
[tex]PN=2(3)[/tex]
[tex]PN=6[/tex]
Therefore, the value of PN is 6 when QN=9.
