ANSWER
[tex] |BE| = 81 \: inches [/tex]
EXPLANATION
In the given, diagram G is called the centroid of the triangle because it is the point where all the three medians of the triangle intersect.
This point, G, divides the medians in the ratio,
[tex]2:1[/tex]
This implies that,
[tex]|BG|:|GE|=2:1[/tex]
or
[tex] \frac{|BG|}{|GE|} = \frac{2}{1} [/tex]
We substitute
[tex]|GE|=27[/tex]
to get,
[tex] \frac{|BG|}{27} = \frac{2}{1} [/tex]
[tex]|BG| = 2 \times 27[/tex]
This will give us,
[tex]|BG| = 54[/tex]
But,
[tex] |BE|=|BG|+|GE|[/tex]
This implies that,
[tex] |BE|=54 + 27[/tex]
[tex] |BE|=81 \: inches[/tex]
Alternatively,
[tex]|BE|:|GE|=3:1[/tex]
Or
[tex] \frac{|BE|} { |GE|} = \frac{3}{1} [/tex]
This gives us,
[tex] |BE| = 3 \times 27[/tex]
[tex] |BE| = 81 \: inches[/tex]
