Answer:
A: FG = ½GC
Step-by-step explanation:
Since AD, BC and CD are medians concurrent at G, it means G is the centroid.
Now, when median passes through the centroid, the centroid divides the median in the ratio of 2:1.
Also,that the median touches the side of the triangle at their midpoints.
Thus,by inspection, we can say that;
GD = ⅓AD
GC/FG = 2/1
Thus, GC = 2FG and FG = ½GC
BG = ⅔BE
Tbus,looking at the options given and what we have gotten in proof, we can say only FG = ½GC is correct.
We will solve using the law of sines as follows:
Now, we solve for X:
![\Rightarrow X=\frac{\sin(60)}{\sin(30)}\Rightarrow X=\sqrt[]{3}](https://tex.z-dn.net/?f=%5CRightarrow%20X%3D%5Cfrac%7B%5Csin%2860%29%7D%7B%5Csin%2830%29%7D%5CRightarrow%20X%3D%5Csqrt%5B%5D%7B3%7D)
So, the length of X is sqrt(3).
Good news: they are all like terms
9x + 5x -3x -8x = 3x
7, you divide the 14 by 2 because the qr is two times the length of gh, therefore 7 is two times the length of fh
