Question

PLEASE HELP :'))

Point R is a centroid of the triangle SQU. If VR = 18 cm, what is UV?

A) 12 cm
B) 36 cm
C) 27 cm
D) 54 cm

Answer 1

D) 54 cm

Explanation:

We can use the Centroid Theorem to solve this problem, which states that the centroid of a triangle is
`(2)/(3)` of the distance from each of the triangle's vertices to the midpoint of the opposite side.

Therefore,
`R` is
`(2)/(3)` of the distance from
`U` to
`V`, since the latter is the midpoint of the side opposite to
`U`. We know this because
`R` belongs to
`UV`, so
`R` must be
`QS`'s midpoint due to the fact that by definition, the centroid of a triangle is the intersection of a triangle's three medians (segments which connect a vertex of a triangle to the midpoint of the side opposite to it).

We can then write the following equation:

`VR=(1)/(3) UV`

Substituting
`VR = 18` into the equation gives us:

`18=(1)/(3) UV`

Solving for
`UV`, we get:

`18=(1)/(3) UV`

`3 *18=3*(1)/(3)UV` (Multiply both sides of the equation by
`3` to get rid of
`UV`'s coefficient)

`54=UV` (Simplify)

`UV=54` (Symmetric Property of Equality)

Therefore, the answer is D. Hope this helps!