Question

if ( bc = 30 ), find the length of ( fe ).

Explanation:

Step1: Apply the Mid - segment Theorem

The Mid - segment Theorem states that the length of a mid - segment (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
In \(\triangle ABC\), \(GD\) is a mid - segment (since \(AG = GB\) and \(AD=DC\)), so \(GD=\frac{1}{2}BC\). Given \(BC = 30\), then \(GD=\frac{1}{2}\times30 = 15\).

Step2: Use the Mid - segment relationship for \(\triangle AGD\)

In \(\triangle AGD\), \(FE\) is a mid - segment (since \(AF = FG\) and \(AE=ED\)). By the Mid - segment Theorem, \(FE=\frac{1}{2}GD\).
Since \(GD = 15\), then \(FE=\frac{1}{2}\times15=7.5\)

Answer:

None of these answers are correct.