Question

in triangle abc, bg = 24 mm. what is the length of segment ge? 12 mm 24 mm 36 mm 48 mm figure may not be drawn to scale

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. Point G is the centroid of triangle ABC and BE is a median. So, BG:GE = 2:1.

Step2: Set up proportion

Let GE = x. Given BG = 24 mm. We have the proportion $\frac{BG}{GE}=\frac{2}{1}$, substituting BG = 24, we get $\frac{24}{x}=\frac{2}{1}$.

Step3: Solve for x

Cross - multiply: 2x = 24, then x = 12 mm.

Answer:

12 mm