Question

PLEASE HELP :'))

Answer 1

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 $\frac{2}{3}$ of the distance from each of the triangle's vertices to the midpoint of the opposite side.

Therefore, $R$ is $\frac{2}{3}$ 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:

$VR=\frac{1}{3} UV$

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

$18=\frac{1}{3} UV$

Solving for $UV$, we get:

$18=\frac{1}{3} UV$

$3 *18=3*\frac{1}{3}UV$ (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!