Answer :
Final answer:
In the triangle TUV, using the properties of a centroid, we can determine that FZ equals 20, and WZ equals 40. This fits into the given values of XZ and WZ.
Explanation:
This question is about the properties of a centroid in a triangle. In a triangle, the centroid, which is the point where all median lines intersect, divides each median into segments with a ratio of 2:1. That means the segment from the centroid to the midpoint of the side (in this case is ZW) has a length that is twice as long as the segment from the centroid to the triangle's vertex (in this case is FZ).
If we apply it to the values given, where TZ equal to 60, and Z is the centroid, then the length of FZ should be 1/3 of 60 which is 20, while the length of ZW should be 2/3 of 60, which is 40.
As given XZ equals 28, then since Z is the centroid, XZ = FZ + ZW = 20 + 40 = 60, so the calculation fits the given values. Similarly, for WZ equals 25, we do the same calculation and find that WZ should also follow the same 2:1 ratio division at the centroid Z and matches the given 25.
Learn more about Centroid in Geometry here:
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