Question 576346
Let's say that the sides of the original square sheet of metal measured x inches.
As you cut those 2 inch by 2 inch squares from the corners, you are left with a center square surrounded by rectangular flaps 2 inches wide, that will fold up to make the sides of the box.
The middle part that will be the bottom of the box is a square with sides measuring (x-4) inches.
{{{drawing( 300,300, -3,30,-3,30,
rectangle(0,0,27,27),
red(line(2,0,2,2)),red(line(2,2,0,2)),red(line(25,0,25,2)),red(line(25,2,27,2)),
red(line(2,25,2,27)),red(line(2,25,0,25)),red(line(25,25,25,27)),red(line(25,25,27,25)),
green(rectangle(2,2,25,25)),
locate(0.5,25,2),locate(25.5,25,2),locate(12,25,x-4),
locate(13,0,x), arrow(13,-1,0,-1),arrow(13.8,-1,27,-1))}}} The volume of the box is the surface area of the green base{{{((x-4)^2)}}} times the height {{{(2)}}},
so {{{2*(x-4)^2=1058}}} --> {{{(x-4)^2=1058/2=529}}} --> {{{x-4=sqrt(529)=23}}},
and if {{{x-4=23}}} --> {{{x=23+4}}}, so {{{highlight(x=27)}}}