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

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,

AG / DG = 2/1

(19x+14)/(9x+20) = 2/1

19x + 14 = 18x + 40

19x - 18x = 40 - 14

x = 26

Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,

GF = DG = 9x+20

GF = DG = 9(26) + 20

GF = 254 units

Hence, the length of GF is 254 units.

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