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 $2:1$, where the segment from the vertex to the centroid is twice the segment from the centroid to the midpoint. So $CG = 2 \cdot DG$.

Step2: Set up equation from given condition

We know $CG = DG + 6$. Substitute $CG = 2 \cdot DG$ into this:
$2DG = DG + 6$

Step3: Solve for DG

Subtract $DG$ from both sides:
$2DG - DG = 6$
$DG = 6$

Step4: Find CG and CD

$CG = 2 \cdot DG = 2 \cdot 6 = 12$
$CD = CG + DG = 12 + 6 = 18$

Answer:

18 units