Answer:
The length of FG is [tex]19\:units[/tex].
Step-by-step explanation:
Since the altitude of the triangle bisects the third side, triangle FGH is isosceles.
Therefore [tex]|FG|=|HG|[/tex]
This implies that,
[tex]5x-6=3x+4[/tex]
This is a linear equation where we easily solve for [tex]x[/tex].
We group like terms to get,
[tex]5x-3x=4+6[/tex]
[tex]2x=10[/tex]
We divide both sides by 2 to obtain,
[tex]x=5[/tex].
The length of FG is
[tex]5(5)-6=25-6=19[/tex]
