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Point G is on line segment FH. Given FG=5x+2,GH=3x-1, and FG=9, determine the numerical length of FG

Sagot :

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]

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