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 into a ratio of \(2:1\), so \(CG = 2 \times DG\).

Step2: Set up equation

Let \(DG = x\), then \(CG = x + 6\). From the centroid property, \(x + 6 = 2x\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(6 = x\), so \(DG = 6\) and \(CG = 12\).

Step4: Find \(CD\)

\(CD = CG + DG = 12 + 6 = 18\) units.

Answer:

18 units