Question

In ABC, GE=27in. What is the length of BE?

Answer 1

ANSWER


`|BE| = 81 \: inches`

Step-by-step 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,

`2:1`

This implies that,


`|BG|:|GE|=2:1`

or


`(|BG|)/(|GE|) = (2)/(1)`

We substitute


`|GE|=27`

to get,


`(|BG|)/(27) = (2)/(1)`



`|BG| = 2 * 27`

This will give us,


`|BG| = 54`

But,


`|BE|=|BG|+|GE|`

This implies that,


`|BE|=54 + 27`


`|BE|=81 \: inches`

Alternatively,


`|BE|:|GE|=3:1`

Or


`\fracBE = (3)/(1)`

This gives us,


`|BE| = 3 * 27`


`|BE| = 81 \: inches`