Answer:
Option 4th is correct
x = 9
Step-by-step explanation:
Using Basic Proportionality theorem:
If a line is drawn parallel to one side of a triangle to intersects the other two side in a distinct point, then the other two sides are divided in the ratio.
As per the statement:
In the given triangle ABC.
[tex]FG || BC[/tex]
Then,
by Basic Proportionality theorem:
[tex]\frac{FA}{FB} = \frac{AG}{GC}[/tex]
Substitute the given values, we have;
[tex]\frac{x+1}{x+6} = \frac{x-1}{x+3}[/tex]
By cross multiply we have;
⇒[tex](x+1)(x+3) = (x-1)(x+6)[/tex]
⇒[tex]x^2+3x+x+3 =x^2+6x-x-6[/tex]
Combine like terms;
[tex]x^2+4x+3 =x^2+5x-6[/tex]
Subtract [tex]x^2[/tex] from both sides we have;
[tex]4x+3 = 5x-6[/tex]
Subtract 5x from both sides we have;
[tex]-x+3 = -6[/tex]
Subtract 3 from both sides we have;
-x = -9
Divide both sides by -1 we have;
x = 9
Therefore, the value of x is, 9
