Given:
In triangle RST, SQ=8 and QT=12.
To find:
The measure of sides SW and UQ.
Solution:
We know that centroid of a triangle is the intersection point of the medians and it divides each median in 2:1.
In the given figure SW and TU are medians and Q is the centroid. So,
[tex]\dfrac{SQ}{QW}=\dfrac{2}{1}[/tex]
[tex]\dfrac{8}{QW}=\dfrac{2}{1}[/tex]
[tex]\dfrac{8}{2}=QW[/tex]
[tex]4=QW[/tex]
Now,
[tex]SW=SQ+QW[/tex]
[tex]SW=8+4[/tex]
[tex]SW=12[/tex]
TU is a median. So,
[tex]\dfrac{QT}{UQ}=\dfrac{2}{1}[/tex]
[tex]\dfrac{12}{UQ}=\dfrac{2}{1}[/tex]
[tex]\dfrac{12}{2}=UQ[/tex]
[tex]6=UQ[/tex]
Therefore, the measure of SW is 12 units and the measure of UQ is 6 units.
