Question

G is Centroid Where medians AD and BE intersect If BG = 10 cm then GE= ?​

Answer 1

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Answer 2

Given:

G is the centroid of a triangle ABC where medians AD and BE intersect.

BG = 10cm

To find:

Length of GE.

Solution:

Centroid is the intersection point of all medians of a triangle. Median is drawn from a vertex to the midpoint of opposite side.

Centroid divides a median in the ratio $2:1$

Here, BE is a median and G is the centroid.

Let G divide BE into BG and GE in the ratio $2:1$.

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

On cross-multiplying,

$BG=2GE$

The value of BG is given as 10cm. Substituting in the above equation:

$10=2GE$

$GE=\frac{10}{2}=5 cm$

Value of GE is 5cm

The length of GE is 5cm where G is the centroid of a triangle, E is the midpoint of side AC and BE is the median to the side AC.