document.write( "Question 1164700: How many sides are there in a polygon if the number of sides equals the number of diagonals? \n" ); document.write( "

Algebra.Com's Answer #789146 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "n sides and    diagonals.\r\n" );
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document.write( "This quantities are equal (given)\r\n" );
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document.write( "    n = \r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    2n = n*(n-3)\r\n" );
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document.write( "    n^2 - 3n - 2n = 0\r\n" );
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document.write( "    n^2 - 5n = 0\r\n" );
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document.write( "    n*(n-5) = 0.\r\n" );
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document.write( "The roots are  n= 0  and  n= 5.\r\n" );
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document.write( "Of them, only n= 5 is interesting for us.\r\n" );
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document.write( "It is the problem's answer.\r\n" );
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document.write( "ANSWER.  5-sided polygon (pentagon).\r\n" );
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