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Vanyuwa [196]
3 years ago
8

PLEASE HELP :'))

Mathematics
1 answer:
andreev551 [17]3 years ago
7 0

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!

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