Question

G is the centroid of triangle ABC. What is the length of AE? ? units

Answer 1

G is the centroid it means that BG/FG=2 (G divides the median with this ratio)
3x+6/2x-1=2
3x+6=4x-2
x=8
then AG=26 then GE=13 so AE=39

Answer 2

we know that

The centroid is the intersection of the three medians in the triangle. The centroid divides each median into two parts, which are always in the ratio $2:1$

Step 1

Find the value of x

$\frac{BG}{GF}=\frac{2}{1} \\ \\\frac{3x+6}{2x-1}=\frac{2}{1}\\ \\3x+6=2(2x-1)\\ \\3 x+6=4x-2\\ \\4 x-3x=6+2\\ \\x =8\ units$

Step 2

Find the value of GE

$\frac{AG}{GE}=\frac{2}{1} \\ \\\frac{2x+10}{GE}=\frac{2}{1}\\ \\2x+10=2GE$

Substitute the value of x

$2x+10=2GE\\2 *8+10=2GE\\GE=13\ units$

Step 3

Find the value of AE

$AE=AG+GE\\AE=(2x+10)+13\\AE=(2*8+10)+13=39\ units$

therefore

the answer is

the length of AE is $39\ units$