# algebra

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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 -

Did you make a sketch?

width of cardboard --- x
length of cardboard -- x+2

width of box = x-4
length of box = x-2
height of box = x

volume = x(x-2)(x-4) = 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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