Question

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

Explanation:

Step1: Recall centroid property

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

Step2: Set up the equation

Set up the equation \(3x - 2=2(x + 5)\).

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: \(x=10 + 2=12\).

Step4: Find DG

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

Answer:

34 units