Question

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

Answer 1

ANSWER

$|BE| = 81 \: inches$

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

$\frac{|BG|}{|GE|} = \frac{2}{1}$

We substitute

$|GE|=27$

to get,

$\frac{|BG|}{27} = \frac{2}{1}$


$|BG| = 2 \times 27$

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

$\frac{|BE|} { |GE|} = \frac{3}{1}$

This gives us,

$|BE| = 3 \times 27$

$|BE| = 81 \: inches$