Question 907696
Steps done here on paper are not very neat, but I found  {{{IJ=36}}}; and knowing the given {{{GI=24}}}, simply using segment addition postulate gives {{{GI+IJ=24+36=highlight(60)}}}.


Note that in my separate work not shown, the ratio relationships given can easily be converted into simple linear equations.
{{{3GH=HI}}}, {{{2HI=IJ}}}.


Also, {{{GH+HI=24}}}
{{{(1/3)HI+HI=24}}}
{{{(4/3)HI=24}}}
{{{HI=(3/4)24}}}
{{{highlight_green(HI=18)}}}