document.write( "Question 1138939: A polygon has 44 diagonals . Find the number of its sides
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Algebra.Com's Answer #756715 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "The number of diagonals of any (convex) polygon is  ,\r\n" );
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document.write( "where \"n\" is the number of sides (vertices).\r\n" );
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document.write( "So, they ask you to find \"n\" from the equation\r\n" );
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document.write( "     = 44.\r\n" );
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document.write( "Simplify and solve for \"n\" :\r\n" );
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document.write( "    n*(n-3) = 44*2 = 88\r\n" );
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document.write( "    n^2 - 3n - 88 = 0\r\n" );
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document.write( "    (n-11)*(n+8) = 0\r\n" );
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document.write( "Of the two roots,  n= 11  and  n= -8,  only positive root n= 11 is meaningful solution to the problem.\r\n" );
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document.write( "ANSWER.  n = 11.  The number of sides and vertices is 11.\r\n" );
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