document.write( "Question 1197396: A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1092 in^3, what were the original dimensions of the piece of metal?
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Algebra.Com's Answer #830642 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four corners
\n" ); document.write( "and the flaps are folded upward to form an open box. If the volume of the box is 1092 in^3, what were the original
\n" ); document.write( "dimensions of the piece of metal? What is the original width?
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document.write( "Let x be the original width of the piece of metal.\r\n" );
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document.write( "Then the original length is (x+15) inches.\r\n" );
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document.write( "After cutting the squares and folding the dimensions of the base of the open box are (x-6) and (x+9) inches \r\n" );
document.write( "(by 2*3 = 6 inches less than the original dimensions).\r\n" );
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document.write( "Therefore, the volume equation is\r\n" );
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document.write( "    3*(x-6)*(x+9) = 1092,\r\n" );
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document.write( "or, equivalently\r\n" );
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document.write( "    (x-6)*(x+9) = 1092/3 = 364.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    x^2 - 6x + 9x - 54 = 364\r\n" );
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document.write( "    x^2 + 3x - 418 = 0\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "It gives two roots, one negative and one positive.\r\n" );
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document.write( "We reject the negative root and accept the positive one  x =  = 19.\r\n" );
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document.write( "ANSWER. The original width was 19 inches.\r\n" );
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document.write( "        The original length was 19 + 15 = 34 inches.\r\n" );
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document.write( "CHECK.  The volume is  3*(19-6)*(34-6) = 3*13*28 = 1092 in^3, which is precisely correct.\r\n" );
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