Question

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

Triangle D E F has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments D C, E B, F A.

[Figure may not be drawn to sacle]

What is DG?

12 units
17 units
34 units
51 units

Answer 1

Answer:

x+5/3x-2= 1/2

2x+10=3x-2

x= 12

DG=34 unit

Answer 2

The value of DG is 34 units.

Step-by-step explanation:

Given:

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

Triangle D E F has centroid G.

Lines are drawn from each point to the midpoint of the opposite side to form line segments D C, E B, F A.

To Find:

The value of DG.

Solution:

Point G is the centroid of the triangle as it is the point where the medians of the triangle are intersecting.

Since the  centroid of a triangle divides its medians in 2:1 ratio.

Therefore, $2(CG) = DG$

Putting the value of CG and DG.

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

$2x +10 = 3x - 2$

$3x - 2x = 10 + 2$

$x = 12$

Substituting  $x=12$ in  $DG = (3x - 2)$ we get,

$DG = (3x - 2)$

        $= 3\times12-2$

        $=36-2$

        $=34\ units$

Thus,the value of DG is 34 units.

PROJECT CODE#SPJ2

         

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