Question

In triangle RST, SQ=8 and QT=12. Find SW and UQ

Answer 1

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,

$\dfrac{SQ}{QW}=\dfrac{2}{1}$

$\dfrac{8}{QW}=\dfrac{2}{1}$

$\dfrac{8}{2}=QW$

$4=QW$

Now,

$SW=SQ+QW$

$SW=8+4$

$SW=12$

TU is a median. So,

$\dfrac{QT}{UQ}=\dfrac{2}{1}$

$\dfrac{12}{UQ}=\dfrac{2}{1}$

$\dfrac{12}{2}=UQ$

$6=UQ$

Therefore, the measure of SW is 12 units and the measure of UQ is 6 units.