Answer:
x = 2
Explanation:
Given:
BG = 27
AG = 13 + 7x
Note that when three perpendicular bisectors of the sides of a triangle meet at a point, the point is called a Circumcenter.
Also, note that the Circumcenter is equidistant from the vertices of the triangle.
So for the given triangle, G is the circumcenter, and AG = BG = CG.
Let's go ahead and solve for x as seen below;
[tex]\begin{gathered} BG=AG \\ 27=13+7x \end{gathered}[/tex]
Let's subtract 13 from both sides of the equation, we'll have;
[tex]\begin{gathered} 27-13=13-13+7x \\ 14=7x \end{gathered}[/tex]
Let's divide both sides by 7;
[tex]\begin{gathered} \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]
So the value of x is 2
