Question

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 sacle

Explanation:

Step1: Identify centroid property

Point $G$ is the centroid, so $DG = 2 \times CG$.

Step2: Substitute given expressions

$3x - 2 = 2(x + 5)$

Step3: Solve for $x$

$3x - 2 = 2x + 10$
$3x - 2x = 10 + 2$
$x = 12$

Step4: Calculate length of $DG$

Substitute $x=12$ into $DG=3x-2$:
$DG = 3(12) - 2$

Answer:

17 units