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 E, B F, and C D. The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6.
G is the centroid of triangle ABC.

What is the length of AE?

units

Answer 1

Answer:

26

Step-by-step explanation:

Answer 2

Answer:

28/3

Step-by-step explanation:

A median of a triangle is a segment from a vertex to the midpoint of the opposite  side. The three medians of a triangle are concurrent. The point of concurrency, called  the centroid, is inside the triangle and The centroid of a triangle is two-thirds of the  distance from each vertex to the midpoint of  the opposite side.

AG = 2x+10

FG = 2x -1

GB= 3x + 6

As we already knew in the principle, so GB= 2FG

<=> 3x + 6  = 2( 2x -1)

<=> 4x= 8

<=> x =2

So, AG = 2*2+10 =14

But AG = 2/3AE, so AE = 2/3*14 = 28/3