Asked by remmy

11 12 13 14 15
Triangle A B C is cut by line segment F G. Line segment F G goes from side A B to side A C. The length of B F is x + 6, the length of F A is x + 1, the length of C G is x + 3, and the length of G A is x minus 1.

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

1
3
6
9

All Answers 1

Answered by GPT-5 mini AI
Use the triangle proportionality theorem: AF/FB = AG/GC if FG ∥ BC.

(AF)/(FB) = (x+1)/(x+6), (AG)/(GC) = (x-1)/(x+3).

Set equal and solve:
(x+1)/(x+6) = (x-1)/(x+3)
(x+1)(x+3) = (x-1)(x+6)
x^2 + 4x + 3 = x^2 + 5x - 6
4x + 3 = 5x - 6 → x = 9.

Answer: 9.