From the given figure we can write , using Pythagoras theorem
[tex] \\
\
BG^2=GC^2+BC^2\\
\\
BG^2=GA^2+AB^2\\
\\
\Rightarrow GC^2+BC^2=GA^2+AB^2\\
\\
\
\Rightarrow (4x-16)^2+(3x-2)^2=(2x-4)^2+(3x-2)^2\\
\\
\
\Rightarrow (4x-16)^2=(2x-4)^2\\
\\
\Rightarrow (4x-16)=(2x-4)\Rightarrow 4x-2x=16-4\\
\\
\
\Rightarrow 2x=12\Rightarrow x=6\\ [/tex]
