Question

In triangle TRS, VZ = 6 inches. What is RZ?

3 inches
6 inches
12 inches
18 inches

Answer 1

Explanation

In the triangle TRS, the point Z is the centroid

RV=RZ+VZ

The property of the centroid states that

RZ=\frac{2}{3} RV\\ \\ VZ=\frac{1}{3} RV

Find the value of RV

we have

VZ=6\ inches

so

RV=3VZ=3*6=18\ inches

Find the value of RZ

RZ=\frac{2}{3} RV\\ \\RZ= \frac{2}{3}*18=12\ inches

therefore

the answer is

RZ is 12\ inches

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Answer 2

we know that

In a triangle, a median is created by a vertex connected to the midpoint of the opposite side. Where all three lines intersect is the centroid, which is also the "center of mass"

In this problem

In the triangle TRS, the point Z is the centroid

`RV=RZ+VZ`

The property of the centroid states that

`RZ=(2)/(3) RV\\ \\ VZ=(1)/(3) RV`

Find the value of RV

we have

`VZ=6\ inches`

so

`RV=3VZ=3*6=18\ inches`

Find the value of RZ

`RZ=(2)/(3) RV\\ \\RZ= (2)/(3)*18=12\ inches`

therefore

the answer is

RZ is
`12\ inches`