document.write( "Question 1102143: An open box is formed from a rectangular piece of cardboard that is 3 in. longer than it is wide, by removing squares of side 2 in. from each corner and folding up the sides. If the volume of the carton is then 216 in^3, what were the dimensions of the original piece of cardboard? \n" ); document.write( "

Algebra.Com's Answer #716794 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The area of the bottom of the box is its volume 216 in^3 divided by the height 2 in:\r\n" );
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document.write( "area =  = 108 square inches.\r\n" );
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document.write( "It is clear that the dimensions of the box are 2+2 = 4 inches less than the dimensions of the original piece of cardboard.\r\n" );
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document.write( "Also, it is clear that the difference of dimensions of the bottom of the box is the same as for the original cardboard, i.e. 3 inches.\r\n" );
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document.write( "So, you need to find two integer numbers that differ in 3 units and multiply up to 108.\r\n" );
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document.write( "This numbers are 9 and 12.\r\n" );
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document.write( "Thus the bottom of the box has the dimensions of 9 in and 12 in.\r\n" );
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document.write( "Then the original cardboard has dimensions 9+4 = 13 inches and 12+4 = 16 inches.\r\n" );
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