in triangle def, cg = (x + 5) units and dg = (3x - 2) units. what is dg? 12 units 17 units 34 units 51 units…

in triangle def, cg = (x + 5) units and dg = (3x - 2) units. what is dg? 12 units 17 units 34 units 51 units figure may not be drawn to scale

in triangle def, cg = (x + 5) units and dg = (3x - 2) units. what is dg? 12 units 17 units 34 units 51 units figure may not be drawn to scale

Answer

Explanation:

Step1: Recall centroid - property

The centroid of a triangle divides each median in a ratio of 2:1. Here, G is the centroid of $\triangle DEF$, so $DG = 2CG$.

Step2: Set up the equation

Set up the equation based on the ratio: $3x - 2=2(x + 5)$.

Step3: Solve the equation

Expand the right - hand side: $3x-2 = 2x+10$. Subtract $2x$ from both sides: $3x-2x-2=2x - 2x+10$, which gives $x-2 = 10$. Then add 2 to both sides: $x=12$.

Step4: Find the length of DG

Substitute $x = 12$ into the expression for DG. $DG=3x - 2=3\times12-2=36 - 2=34$.

Answer:

34 units