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Lelu [443]
3 years ago
11

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

ther lengths.

Mathematics
1 answer:
nadezda [96]3 years ago
4 0

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

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