Question 1060643
Dimensions x and y
Uniform sidelength of each square, w
Volume of box, v


w is also how high or tall the box.
Bottom area when flaps folded will be  {{{(x-2w)(y-2w)}}}


MAIN STARTING EQUATION:  {{{w(x-2w)(y-2w)=v}}}


STEPS

{{{w(xy-2yw-2xw+4w^2)-v=0}}}

{{{xyw-2yw^2-2xw^2+4w^3-v=0}}}

{{{4w^3-2(x+y)w^2+xyw-v=0}}}-------Cubic equation in the unknown variable, w.


Make the substitutions and simplify from {{{system(x=20,y=30,v=1008)}}} and the equation becomes  {{{w^3-25w^2+150w-252=0}}}.


You can try looking for zeros or roots based on Rational Roots theorem.  The practical factorizations which would be useful for the term,  {{{-252}}} would be  {{{252=2*126=3*84=4*63=6*42}}}; so continue this by testing roots  1, 2, 3, 4, 6, 7, and see if any give remainder of 0 when using synthetic division.



(3 and 4.92 both will work).