Answer:
D) 54 cm
Step-by-step explanation:
We can use the Centroid Theorem to solve this problem, which states that the centroid of a triangle is [tex]\frac{2}{3}[/tex] of the distance from each of the triangle's vertices to the midpoint of the opposite side.
Therefore, [tex]R[/tex] is [tex]\frac{2}{3}[/tex] of the distance from [tex]U[/tex] to [tex]V[/tex], since the latter is the midpoint of the side opposite to [tex]U[/tex]. We know this because [tex]R[/tex] belongs to [tex]UV[/tex], so [tex]R[/tex] must be [tex]QS[/tex]'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:
[tex]VR=\frac{1}{3} UV[/tex]
Substituting [tex]VR = 18[/tex] into the equation gives us:
[tex]18=\frac{1}{3} UV[/tex]
Solving for [tex]UV[/tex], we get:
[tex]18=\frac{1}{3} UV[/tex]
[tex]3 *18=3*\frac{1}{3}UV[/tex] (Multiply both sides of the equation by [tex]3[/tex] to get rid of [tex]UV[/tex]'s coefficient)
[tex]54=UV[/tex] (Simplify)
[tex]UV=54[/tex] (Symmetric Property of Equality)
Therefore, the answer is D. Hope this helps!
