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 [tex]2:1[/tex]
Step 1
Find the value of x
[tex]\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[/tex]
Step 2
Find the value of GE
[tex]\frac{AG}{GE}=\frac{2}{1} \\ \\\frac{2x+10}{GE}=\frac{2}{1}\\ \\2x+10=2GE\\\\[/tex]
Substitute the value of x
[tex]2x+10=2GE\\2 *8+10=2GE\\GE=13\ units[/tex]
Step 3
Find the value of AE
[tex]AE=AG+GE\\AE=(2x+10)+13\\AE=(2*8+10)+13=39\ units[/tex]
therefore
the answer is
the length of AE is [tex]39\ units[/tex]
