Posted by cantu on Monday, May 7, 2012 at 8:55am.
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
after cut-out
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
Wolfram ,,,,,,
http://www.wolframalpha.com/input/?i=x%5E3+-+3x%5E2+%2B+2x+-+20+%3D+0
and got
x = appr. 3.837
so the cardboard was 3.837 by 7.674
check:
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.
thank you
oddly enough, I did exactly what you did! Then when I saw the messy answer, I reread the problem.
Related Questions
calculus - Help!!! A rectangle piece of cardboard twice as long as wide is to be...
maths - 1. You are cutting colored cardboard rectangles for school art show. ...
geometry - how many inches long is the radius of the largest circle that can fit...
Algebra - A ribbon 106 inches long is cut into three pieces. The middle-sized ...
math - a piece of cardboard is twice as it is wide. It is to be made into a box ...
college algebra - how do you slove this problem a rope is 72 feet long is cut ...
Math algebra - A 120- foot long rope is cut into three pieces the first piece of...
algebra - a cable is cut into 2 pieces. One piece is twice as long as the other ...
Algebra - A rope 116 inches is cut into three pieces.The middle-sized piece is ...
algebra - A 30ft. cable is cut into 2 pieces. One piece is twice as long as the ...
For Further Reading
