Question

Which value of x would make Line segment F G is parallel to line segment B C?

Answer 1

option 4, X=9

Explanation:

Answer 2

x = 9

Explanation:

Consider the below figure attached with his question.

In the below figure
`FA=x+1, FB=x+6, GA=x-1\text{ and }GC=x+3`.

According to Basic Proportionality Theorem (BPT), if a line is parallel to one side of a triangle, then it divides the two remaining sides in the same ratio.

Using BPT theorem,

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

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

On cross multiplication we get

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

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

`4x+3=5x-6`

`4x-5x=-6-3`

`-x=-9`

`x=9`

Hence, FG║BC if the value of x is 9.