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

Question

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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

Mathematics

1 answer:

Helga [31] · Answer 1 · 2023-10-29T17:15:34+03:00

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

<h3>How to find the length of GF?</h3>

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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