document.write( "Question 486511: an open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. if the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal? \r
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Algebra.Com's Answer #332553 by Edwin McCravy(20055)\"\" \"About 
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an open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. if the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?\r
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document.write( "We start with this square. Let the square have dimensions s ft × s ft\r\n" );
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document.write( "We partition it this way, the squares to cut out are 1 ft each, and\r\n" );
document.write( "there are two from each side so the middle piece is s-2\r\n" );
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document.write( "Then we cut away the squares and have this:\r\n" );
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document.write( "When we fold up the flaps we will have a rectangular solid\r\n" );
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document.write( "whose length = L = s-2, whose width = W = s-2, and whose height = H = 1\r\n" );
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document.write( "V = LWH\r\n" );
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document.write( "and we are given that the volume of the box is 4 cubic feet, so\r\n" );
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document.write( "4 = (s-2)(s-2)(1)\r\n" );
document.write( "4 = (s-2)(s-2)\r\n" );
document.write( "4 = s²-2s-2s+4\r\n" );
document.write( "4 = s²-4s+4\r\n" );
document.write( "0 = s²-4s\r\n" );
document.write( "0 = s(s-4)\r\n" );
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document.write( "s = 0  s-4 = 0\r\n" );
document.write( "       s = 4\r\n" );
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document.write( "We ignore the zero solution.  So the sheet to cut \r\n" );
document.write( "should be 4 ft × 4 ft.\r\n" );
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document.write( "Edwin
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