If FG = 9, GH = 4x, and FH = 7x, what is GH?

[math_celebrity]

If FG = 9, GH = 4x, and FH = 7x, what is GH?

By segment addition, we have:
FG + GH = FH

Substituting in the values given, we have:
9 + 4x = 7x

To solve this equation for x, we type it in our math engine and we get:
x = 3

The question asks for GH, so with x = 3, we have:
GH = 4(3)
GH = 12