Question 944103
Dimensions will be w and 2w, as variables.


Forming the open box, the volume is {{{(w-2*1)(2w-2*1)w=144}}};
{{{(w-2)(2w-2)w=144}}}
{{{(2w^2-2w-4w+4)w-144=0}}}
{{{2w^3-6w^2+4w-144=0}}}
{{{highlight_green(w^3-3w^2+2w-72=0)}}}


You would next make of list of possible rational roots to check, and use synthetic division to find which root will work.


Instead of actually doing that, I am using the graphing feature of google.com to inspect the graph of the function for roots or zeros.  (Replacement of w with x is necessary there.)


The root may be irrational, appearing to be extremely near to 5.24.
Maybe 5.24028...