Given:
Point G is the centroid of triangle ABC.
FG = x + 8 and AG = 6x - 4
To find:
The value of the variable x.
Solution:
Using rule of centroid:
[tex]$\Rightarrow A G=\frac{2}{3} A F[/tex]
[tex]$\Rightarrow A G=\frac{2}{3}(A G+F G)[/tex]
[tex]$\Rightarrow 6 x-4=\frac{2}{3}(6 x-4+x+8)[/tex]
[tex]$\Rightarrow 6 x-4=\frac{2}{3}(7 x+4)[/tex]
Multiply by 3 on both sides, we get
⇒ 3(6x - 4) = 2(7x + 4)
⇒ 18x - 12 = 14x + 8
Subtract 14x from both sides.
⇒ 4x - 12 = 8
Add 12 on both sides.
⇒ 4x = 20
Divide by 4 on both sides.
⇒ x = 5
The value of x is 5.
