Answer:
FG=30
Step-by-step explanation:
Since we know that Point G is on the Segment FH, it doesn't really matter where G is, but we can know for certain that:
[tex]FH=FG+GH[/tex]
We are given that FH is 4x, GH is x, and FG is 2x+10. Substitute:
[tex]4x=(2x+10)+x[/tex]
Solve for x. On the right, combine like terms:
[tex]4x=3x+10[/tex]
Subtract 3x from both sides:
[tex]x=10[/tex]
So, the value of x is 10.
To find the value of FG, substitute 10 into its x:
[tex]FG=2x+10\\FG=2(10)+10[/tex]
Multiply:
[tex]FG=20+10[/tex]
Add:
[tex]FG=30[/tex]
And we're done!
