Question

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

Answer 1

Given:

FG=5x+2

GH=3x-1

FG=9

Let us draw the line segment as follows,

Equating the length of FG, we get,

`\begin{gathered} 5x+2=9 \\ 5x=9-2 \\ 5x=7 \\ x=(7)/(5) \end{gathered}`

Substitute the value of x in the given value of GH,

`\begin{gathered} GH=3x-1 \\ =3((7)/(5))-1 \\ =(21)/(5)-1 \\ =(16)/(5) \\ =3.2 \end{gathered}`

And the total length FH is,

`\begin{gathered} FH=FG+GH \\ =9+3.2 \\ =12.2 \end{gathered}`

Hence, the lengths are,

`\begin{gathered} FG=9 \\ GH=3.2 \\ FH=12.2 \end{gathered}`