The Triangle RST is missing, so i have attached it.
Answer:
A) TZ = 34
B) ZW = 17
C) SY = 69
D) XZ = 21
Step-by-step explanation:
To form the centroid, we see median drawn from the centre of all three sides.
Thus means the 3 sides are divided into 2 and as such;
XS = XT
YR = YT
WR = WT
Now, for median that forms centroid, the two parts are usually not the same length but instead in the ratio 2:1. That means one portion of the line segment is twice the length of the other.
Thus, by inspection of the given triangle, we can say that;
SZ = 2(ZY)
TZ = 2(ZW)
RZ = 2(XZ)
A) Now, we are given TW = 51
TW is made up of TZ and ZW
But since TZ : ZW = 2:1, it means that;
TZ = ⅔ × TW
TZ = ⅔ × 51
TZ = 34
B) From earlier, we saw that TZ = 2(ZW).
Thus; 34 = 2(ZW)
ZW = 34/2
ZW = 17
C) We are given ZY = 23.
From earlier, we saw that;SZ = 2(ZY)
Thus; SZ = 2(23)
SZ = 46
From the attached image we can see that;
SY = SZ + ZY
Thus;
SY = 46 + 23
SY = 69
D) We are given RZ = 42.
From earlier, we saw that;
RZ = 2(XZ)
Thus;
42 = 2(XZ)
XZ = 42/2
XZ = 21
