Given:
FG=5x+2
GH=3x-1
FG=9
Let us draw the line segment as follows,
Equating the length of FG, we get,
[tex]\begin{gathered} 5x+2=9 \\ 5x=9-2 \\ 5x=7 \\ x=\frac{7}{5} \end{gathered}[/tex]Substitute the value of x in the given value of GH,
[tex]\begin{gathered} GH=3x-1 \\ =3(\frac{7}{5})-1 \\ =\frac{21}{5}-1 \\ =\frac{16}{5} \\ =3.2 \end{gathered}[/tex]And the total length FH is,
[tex]\begin{gathered} FH=FG+GH \\ =9+3.2 \\ =12.2 \end{gathered}[/tex]Hence, the lengths are,
[tex]\begin{gathered} FG=9 \\ GH=3.2 \\ FH=12.2 \end{gathered}[/tex]