Answer: 20
Step-by-step explanation:
Given: Point [tex]\text{G}[/tex] is on line segment [tex]\text{FH}[/tex]. Given [tex]\text{FH}[/tex] is [tex]4\text{x}+8[/tex] , [tex]\text{FG}[/tex]. is [tex]\text{x}[/tex], and [tex]\text{GH}[/tex] is [tex]5\text{x}[/tex].
To Find: the numerical length for [tex]\text{GH}[/tex].
Solution:
Point [tex]\text{G}[/tex] is on the line segment [tex]\text{FH}[/tex]
therefore,
[tex]\text{FH}=\text{FG}+\text{GH}[/tex]
putting the values
[tex]4\text{x}+8=\text{x}+5\text{x}[/tex]
[tex]4\text{x}+8=6\text{x}[/tex]
[tex]8=2\text{x}[/tex]
[tex]\text{x}=4[/tex]
Now,
[tex]\text{GH}=5\text{x}[/tex]
[tex]\text{GH}=5\times4[/tex]
[tex]\text{GH}=20[/tex]
Hence numerical length of line segment [tex]\text{GH}[/tex] is [tex]20[/tex]
