document.write( "Question 1135084: The perimeter of a triangle cannot be more than
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Algebra.Com's Answer #752643 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "As other tutor instructed you, you have this inequality\r\n" );
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document.write( "    x + 2x + 21 <= 57      (1)\r\n" );
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document.write( "for the \"second\" side length x.\r\n" );
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document.write( "From this inequality, you immediately get\r\n" );
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document.write( "    3x <= 57 - 21 = 36,   so  x <= 36/3 = 12.\r\n" );
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document.write( "It answers the problem's question, but it is not a COMPLETE DESCRIPTION of possible triangles.\r\n" );
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document.write( "For example,  the sides  1, 2 and 21  satisfy the basic given inequality (1),\r\n" );
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document.write( "but they  DO NOT FORM any triangle - since they do not satisfy another triangle inequality \r\n" );
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document.write( "    x + 2x > 21.      (2)\r\n" );
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document.write( "The inequality (2) requires  3x > 21,  which implies  x > 7.\r\n" );
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document.write( "So, only if the compound inequality holds\r\n" );
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document.write( "    7 < x <= 12,\r\n" );
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document.write( "the described triangle does exist.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my post is THIS :\r
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document.write( "    When you solve problems for triangle side lengths,  you must satisfy and check ALL TRIANGLE inequalities.\r\n" );
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