width = w
length = 2w
(w-2)(2w-2)(1) = 40
(w-1)(w-2) = 20
20 = 4x5, so w = 6
The box is 6 x 12
check: cut off the 1" corners and you get a box 4x10
width --- x
length ---- 2x
width = x-2
length = 2x-2
height = x
volume = x(x-2)(2x-2) = 40
2x^3 - 6x^2 + 4x = 40
x^3 - 3x^2 + 2x - 20 = 0
tried ±1, ±2, ±4, ±5 and could not find a "nice" solution, so I ran it through
x = appr. 3.837
so the cardboard was 3.837 by 7.674
width of box = 3.837-2 = 1.837
length of box =7.674-2 = 5.674
height = 3.837
vol = 1.837x5.674x3.837 =39.99 , not bad
forget my solution,
I was thinking of an entirely different question.
oddly enough, I did exactly what you did! Then when I saw the messy answer, I reread the problem.
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