Point G is on line segment FH. Given FH=4x+8,FG=x,and GH=5x, determine the numerical length for GH

Answer: 20Step-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]