Answer:
Step-by-step explanation:
We will use two properties to solve this problem,
1). Medians of a triangle bisect the sides of a triangle.
2). Centroid of a triangle divides the medians in the ratio of 2 : 1.
Length of FH = 2 × Length of HX
= 2 × 12
FH = 24
PF : PZ = 2 : 1
[tex]\frac{PF}{PZ}=\frac{2}{1}[/tex]
[tex]\frac{PF}{4}=\frac{2}{1}[/tex]
PF = 8
GX = GP + PX
GP = 9 [Given]
Since, [tex]\frac{GP}{PX}=\frac{2}{1}[/tex]
PX = [tex]\frac{9}{2}[/tex] = 4.5
Therefore, GX = 9 + 4.5
GX = 13.5
The other lengths using the centroid theorem gives us;
FH = 24
PF = 8
GX = 13.5
The centroid of a triangle is defined as the point where the three medians intersect each other.
Now, the centroid theorem states that the centroid is ²/₃ of the distance from each vertex to the midpoint of the opposite side.
Thus, applying the centroid theorem to the given triangle gives;
FH = 2(HX)
We see that HX = 12.
Thus; FH = 2 * 12
FH = 24
Also; PF = 2(PZ)
We see that; PZ = 4
Thus;
PF = 2(4)
PF = 8
Also, GP = 2(PX)
We have GP = 9.
Thus;
9 = 2(PX)
PX = 9/2
PX = 4.5
GX = GP + PX
GX = 9 + 4.5
GX = 13.5
Read more at; https://brainly.com/question/24246680
