Question

In  △ABC

, GE=27 in.

 

What is the length of  BE ¯¯¯¯¯ ?

Answer 1

I hope it's not to late but the answer would be 81

Answer 2

BE = 81

Explanation:

From the graph we can see that point G is the barycentre of the triangle, because it's formed by the intersection of the three medians of the triangle, which are defined as segments from a vertex to the midpoint of the opposite side.

From the intersection of all triangle medians we have that:

`BG=2GE`

`CG=2GF`

`AG=2GD`

Also, we know by hypothesis that
`GE=27`. Replacing this value:

`BG=2GE`

`BG=2(27)=54`

Then, by sum of segments, we have:

`BE=BG+GE`

`BE=54+27=81.`

Therefore, BE = 81.