Question

The diagram shows FGH, its medians, centroid P, and the lengths of some of the subsegments. Apply the Centroid Theorem to find other lengths.

Answer 1

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

$\frac{PF}{PZ}=\frac{2}{1}$

$\frac{PF}{4}=\frac{2}{1}$

PF = 8

GX = GP + PX

GP = 9  [Given]

Since, $\frac{GP}{PX}=\frac{2}{1}$

PX = $\frac{9}{2}$ = 4.5

Therefore, GX = 9 + 4.5

GX = 13.5