point g is the centroid of triangle abc. the length of segment cg is 6 units greater than the length of…

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

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

Answer

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, we have $CD = 3\times6=18$ units.

Answer:

18 units