Final answer:
Using the centroid properties of dividing medians in a 2:1 ratio, we have calculated the lengths of various segments in the triangle: WZ is 58 units, ZR is 29 units, SZ is 26 units, ZY is 13 units, and YT remains 48 units.
Step-by-step explanation:
The student's question involves finding the lengths of line segments in a triangle where the centroid is given along with the lengths of certain segments.
In a triangle, the centroid, which is the point where the medians intersect, divides each median into two segments, with the segment from the vertex to the centroid being twice the length of the segment from the centroid to the midpoint of the opposite side.
If Z is the centroid of triangle WXY, and given that WR = 87, SY = 39, and YT = 48, we can find the lengths of other segments using the centroid properties.
- Since Z is the centroid, Z divides WR into two segments:
- WZ and ZR. Since ZR is part of the median, WZ will be twice as long as ZR.
- Hence, ZR = WR/3
- = 87/3
- = 29 units
- and WZ = 2 * ZR = 2 * 29
- = 58 units.
- Similarly, Z divides SY into SZ and ZY, with ZY being one-third the length of SY since it's from the centroid to the midpoint.
- So, ZY = SY/3
- = 39/3 = 13 units, and
- SZ = 2 * ZY
- = 2 * 13
- = 26 units.
- The length of the entire side YT is given, so we don't need to divide it because it's not a median.
To summarize, the lengths of the segments are determined by the centroid division property:
WZ = 58 units, ZR = 29 units, SZ = 26 units, and ZY = 13 units.
YT remains 48 units as that's already a given side length and not part of a median.