Question

point g is the centroid of triangle abc. the length of segment cg is 6 units greater than the length of segment dg. what is cd? 6 units 12 units 18 units 24 units

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1. That is, \(CG = 2DG\).

Step2: Set up an equation

We know that \(CG=DG + 6\). Substitute \(CG = 2DG\) into this equation: \(2DG=DG + 6\).

Step3: Solve for \(DG\)

Subtract \(DG\) from both sides of the equation \(2DG=DG + 6\). We get \(2DG - DG=6\), so \(DG = 6\) units.

Step4: Find \(CD\)

Since \(CD=CG + DG\) and \(CG = 2DG\), then \(CD=2DG+DG=3DG\). Substitute \(DG = 6\) into the equation, so \(CD = 3\times6=18\) units.

Answer:

18 units