Question

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

What is DG?


_____ units

Answer 1

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



What is DG?


___34__ units

Answer 2

34 units.

Explanation:

We have been given an image of a triangle and we are asked to find the length of segment DG,

We can see that point g is the centroid of our given triangle as it is the point, where 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`

`2x-2x+10=3x-2x-2`

`10=x-2`

`10+2=x-2+2`

`12=x`

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

`DG=3x-2`

`DG=3*12-2`

`DG=36-2`

`DG=34`

Therefore, the length of segment DG is 34 units.