document.write( "Question 1204755: an open box is made from a 40-cm by 80-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 2964 cm^2. What is the length of the sides of the squares \n" ); document.write( "

Algebra.Com's Answer #841220 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "an open box is made from a 40-cm by 80-cm piece of tin by cutting a square from each corner
\n" ); document.write( "and folding up the edges. The area of the resulting base is 2964 cm^2.
\n" ); document.write( "What is the length of the sides of the squares
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document.write( "After cutting the squares from the corners and folding,\r\n" );
document.write( "the dimensions of the base are (40-2x) cm and (80-2x) cm,\r\n" );
document.write( "where x is the side of each square.\r\n" );
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document.write( "Now you write this quadratic equation for the base area\r\n" );
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document.write( "    (40-2x)*(80-2x) = 2964  square centimeters.\r\n" );
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document.write( "Then you simplify it step by step\r\n" );
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document.write( "    (20-x)*(40-x) = 741\r\n" );
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document.write( "     800 - 40x - 20x + x^2 = 741\r\n" );
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document.write( "     x^2 - 60x + 59 = 0\r\n" );
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document.write( "     (x-59)*(x-1) = 0\r\n" );
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document.write( "and find the roots  59 and 1.\r\n" );
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document.write( "The root 59 is too big to be the side of the cut square,\r\n" );
document.write( "so the only solution to the problem is 1 cm for the side of the squares.\r\n" );
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document.write( "CHECK.  (40-2*1)*(80-2*1) = 2964 cm^2, the area of the base.  ! correct !\r\n" );
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