Posted by Firdous on Monday, April 29, 2013 at 5:43am.
A rectangular piece of cardboard is 2 units longer than it is wide?
From each of its corner a square piece 2 units on a side is cut out.The flaps are then turned up to form an open box that has a volume of 70 cubic units.Find the length and width of the original piece of cardboard.

algebra  Reiny, Monday, April 29, 2013 at 9:51am
Did you make a sketch?
width of cardboard  x
length of cardboard  x+2
width of box = x4
length of box = x2
height of box = x
volume = x(x2)(x4) = 70
x^3  6x^2 + 8x  70 = 0
That was easy so far, but now we have a nasty cubic.
I tried factors of 70 , no luck
so I used Wolfram to find
x = appr 6.4442
original widht = 6.442
original length = 8.442
http://www.wolframalpha.com/input/?i=x%5E3++6x%5E2+%2B+8x++70+%3D+0
check:
original widht = 6.442
original length = 8.442
box base is 2.4442 by 4.4442
volume = 2.4442 x 4.4442 x 6.4442 = 70.00002 , not bad
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