Question

Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.

What is the length of GF?

units

Answer 1

Based on the calculations, the length of GF is equal to 26 units.

How to find the length of GF?

In Geometry, the centroid of any triangle always divides the lines in a ratio of 2:1. Thus, G divides line B F as follows:

2DG = BD

2(9x + 2) = 40

18x + 4 = 40

18x = 40 - 4

x = 36/18

x = 2.

Similarly, G divides line A F as follows:

2GF = A F

GF = A F/2

GF = (19x + 14)/2

GF = (19(2) + 14)/2

GF = 52/2

GF = 26 units.

Read more on centroid here: brainly.com/question/15015349

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