ANSWER
[tex]|FG| = 19 \: units[/tex]
EXPLANATION
Since the altitude, |GJ| bisects the base of the triangle, it follows that, the triangle is an isosceles triangle.
This implies that,.
[tex]|FG|=|GH|[/tex]
In terms of x, we have the equation.
[tex]5x - 6 = 3x + 4[/tex]
We now group like terms to obtain,
[tex]5x - 3x = 4 + 6[/tex]
This implies that,
[tex]2x = 10[/tex]
Let us divide through by 2 to get,
[tex]x = 5[/tex]
We can see from the diagram that,
[tex]|FG|=5x-6[/tex]
We substitute x=5 to get,
[tex]|FG|=5(5)-6[/tex]
This simplifies to,
[tex]|FG|=25-6[/tex]
[tex]|FG|=19 \: units[/tex]
