Question

Bro I really need this answer (I’ll mark brainliest)

Answer 1

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:

$\Rightarrow A G=\frac{2}{3} A F$

$\Rightarrow A G=\frac{2}{3}(A G+F G)$

$\Rightarrow 6 x-4=\frac{2}{3}(6 x-4+x+8)$

$\Rightarrow 6 x-4=\frac{2}{3}(7 x+4)$

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.