document.write( "Question 1137244: An open box is made from a 30-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
\n" ); document.write( "1776cm^2. What is the length of the sides of the squares in cm? \n" ); document.write( "

Algebra.Com's Answer #755106 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "Mathematical model is this equation\r\n" );
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document.write( "    (30-2x)*(80-2x) = 1776,\r\n" );
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document.write( "where x is the length of the square under the question.\r\n" );
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document.write( "Simplify and solve, step by step\r\n" );
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document.write( "    2400 - 160x - 60x + 4x^2 = 1776\r\n" );
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document.write( "    4x^2 - 220x + 2400 - 1776 = 0\r\n" );
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document.write( "    4x^2 - 220x + 624 = 0\r\n" );
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document.write( "    x^2 - 55x + 156 = 0\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "The two roots are  52  and  3.\r\n" );
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document.write( "Of them, only x= 3 is meaningful.\r\n" );
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document.write( "(The other root x= 52 makes the dimensions of the new base negative !).\r\n" );
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document.write( "ANSWER.  the side of the square is 3 cm.\r\n" );
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document.write( "CHECK.   (30-2*3)*(80-2*3) = 24*74 = 1776 square centimeters.   ! Correct !\r\n" );
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