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 median property

In a triangle, the medians intersect at the centroid, which divides each median into a ratio of \(2:1\) (the longer segment is twice the shorter one). Here, \(G\) is the centroid, so \(DG = 2 \times CG\).

Step2: Set up equation

Given \(CG=(x + 5)\) and \(DG=(3x - 2)\), using the centroid property: \(3x-2=2(x + 5)\)

Step3: Solve for \(x\)

Expand the right side: \(3x-2 = 2x+10\)
Subtract \(2x\) from both sides: \(3x-2x-2=2x - 2x+10\) → \(x - 2=10\)
Add 2 to both sides: \(x-2 + 2=10 + 2\) → \(x = 12\)

Step4: Find \(DG\)

Substitute \(x = 12\) into \(DG=(3x - 2)\): \(DG=3(12)-2=36 - 2=34\)

Answer:

34 units