we know that
The point G is where all \(3\) medians intersect and is often described as the triangle's center of gravity or centroid. It is formed by the intersection of the medians. The centroid divides each median in a ratio of \(2:1\)
so
\(\frac{BG}{GE} =\frac{2}{1} \\\\ GE =\frac{BG}{2}\)
\(BG= 24\ mm\)
substitute in the formula above
\(GE =\frac{24}{2}\)
\(GE= 12\ mm\)
therefore
the answer is
\(GE= 12\ mm\)
