In triangle DEF, CG = (x + 5) units and DG = (3x - 2). What is DG?
12 units, 17 units, 34 units, 51 units

finding the length using the centroid of the triangle

Solution:

Given CG = (x + 5) and DG = (3x - 2)

We can see that point G is the centroid of our given triangle as it is the point where the medians of our given triangle are intersecting.

Since we know that centroid of a triangle divides its medians in 2:1 ratio 

So we can set an equation for DG and CG as:

⇒ 2(CG) = DG

Now let us solve for x.

2(x + 5) = 3x - 2

2x +10 = 3x - 2

Combine like terms

3x - 2x = 10 + 2

x = 12

Upon substituting x = 12 in the expression for the length of segment DG we will get,

DG = 3x - 2

= 3(12) - 2

= 36 - 2

DG = 34 units

Therefore, the length of segment DG is 34 units.

In triangle DEF, CG = (x + 5) units and DG = (3x - 2). What is DG?

Summary:

If in a triangle DEF, CG = (x + 5) units and DG = (3x - 2) then DG is 34 units.

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