Question

In ABC, G is the intersection of the three medians. If CD= 36, find GD.

Answer 1

In triangle ABC, G is the intersection of the three medians. The ratio of GD to CD is 2:1. Given CD = 36, we can find GD.

Step-by-step explanation:

In triangle ABC, G is the intersection of the three medians. The medians of a triangle are the line segments that connect each vertex to the midpoint of the opposite side. Since G is the intersection of the medians, it divides each median into two segments with the ratio 2:1.

Let GD represent the segment of the median that is closer to vertex D. Since the ratio of GD to CD is 2:1, we can set up the following proportion:

GD/CD = 2/1

Substituting the given value CD = 36, we get:

GD/36 = 2/1

Cross-multiplying, we find:

GD = 2 * 36 = 72

Therefore, GD = 72.