Answer:
34 units.
Step-by-step 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:
[tex]2*CG=DG[/tex]
Now let us solve for x.
[tex]2(x+5)=3x-2[/tex]
[tex]2x+10=3x-2[/tex]
[tex]2x-2x+10=3x-2x-2[/tex]
[tex]10=x-2[/tex]
[tex]10+2=x-2+2[/tex]
[tex]12=x[/tex]
Upon substituting x=12 in the expression for the length of segment DG we will get,
[tex]DG=3x-2[/tex]
[tex]DG=3*12-2[/tex]
[tex]DG=36-2[/tex]
[tex]DG=34[/tex]
Therefore, the length of segment DG is 34 units.
