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3 years ago

Triangle QRS has medians QU, RV, and ST. If the measure of segment RW is 18 meters, what is the length of segment RV?

Mathematics

1 answer:

rodikova [14]3 years ago

8 0

Answer: RV = 27 meters

Step-by-step explanation: Median is a line which unites a vertice and a midpoint of the opposite side. The point where, in a triangle, the medians intersect is called Centroid. The centroid divides the median in a ratio of 2:1, so Centroid Theorem states that the centroid of the triangle is at 2/3 of a distance from the vertex to the midpoint of the sides.

The attached figure shows the medians and centroid.

RW and WV are components of RV, the median.

If RW is 18 and following the theorem:

RW = $\frac{2}{3}$ .RV

RV = $\frac{3}{2}$ . RW

RV = $\frac{3}{2}.18$

RV = 27

The median RV measures 27 meters.

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$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}$

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Where:

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$= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA$

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