Question

Which value of x would make ?

1
3
6
9

Answer 1

answer is 9

Explanation:

Answer 2

Option 4th is correct

x = 9

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.

`FG || BC`

Then,

by Basic Proportionality theorem:

`(FA)/(FB) = (AG)/(GC)`

Substitute the given values, we have;

`(x+1)/(x+6) = (x-1)/(x+3)`

By cross multiply we have;

⇒
`(x+1)(x+3) = (x-1)(x+6)`

⇒
`x^2+3x+x+3 =x^2+6x-x-6`

Combine like terms;

`x^2+4x+3 =x^2+5x-6`

Subtract
`x^2` from both sides we have;

`4x+3 = 5x-6`

Subtract 5x from both sides we have;

`-x+3 = -6`

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