document.write( "Question 1207601: 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 5 cubic feet, what should be the dimension of the sheet metal? \r
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Algebra.Com's Answer #845659 by MathTherapy(10552)\"\" \"About 
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document.write( "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 5 cubic feet, what should be the dimension of the sheet metal? \r\n" );
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document.write( "Note: This is a popular problem found in many textbooks but I haven't found one decent explanation. Can someone solve this application one step at a time?\r\n" );
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document.write( "Since the dimensions of the sheet metal are being sought, we let the width, which is also the same measure as\r\n" );
document.write( "the length (the sheet metal is SQUARE), be W\r\n" );
document.write( "As a 1-foot square piece is removed from each end of the sheet metal, the width and the length of the base/bottom\r\n" );
document.write( "of the box will be W - 2, each.\r\n" );
document.write( "The sides/height of the box will be formed from the 1-foot cut-outs \r\n" );
document.write( "So, as the open box will have a volume (Length * Width * Height, or LWH) of 5 cubic feet, we get:\r\n" );
document.write( "L*W*H = 5. Now, with W (width) = W - 2 (same measure as the length, or L), LWH = 5 becomes:\r\n" );
document.write( "(W - 2)(W - 2)(1) = 5\r\n" );
document.write( "       (W - 2)2 = 5 \r\n" );
document.write( "   W2 - 4W + 4 = 5 \r\n" );
document.write( "   W2 - 4W - 1 = 0\r\n" );
document.write( "As the above quadratic cannot be factored with INTEGERS, solutions can be derived by using the quadratic equation \r\n" );
document.write( "formula or completing the square. Using the former, we get: \"matrix%281%2C3%2C+W%2C+%22=%22%2C+%28-+b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29%29\"                                     \r\n" );
document.write( "                                , with \"matrix%283%2C3%2C+a%2C+%22=%22%2C+1%2C+b%2C+%22=%22%2C+-+4%2C+c%2C+%22=%22%2C+-+1%29\"\r\n" );
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document.write( "Width/Length of sheet metal, or    or  \"matrix%281%2C3%2C+W%2C+%22=%22%2C+2+-+sqrt%285%29%29\" <=== IGNORE/REJECT as\r\n" );
document.write( "                                                                                   length|width CANNOT be negative (<0) \r\n" );
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document.write( "  Dimensions of sheet metal:
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