document.write( "Question 996978: If a polygon has 44 diagonals then the no. of its sides is ? \n" ); document.write( "

Algebra.Com's Answer #615226 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "recall:
\n" ); document.write( "Polygon with $\"n\"$ sides has $\"n%28n-3%29%2F2\"$ diagonals\r
\n" ); document.write( "\n" ); document.write( "so, the polygon with $\"44\"$ diagonals will have:\r
\n" ); document.write( "\n" ); document.write( " $\"44+=+n%28n-3%29%2F2\"$ ...solve for $\"n\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"88+=+n%28n-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"88+=+n%5E2-3n\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"n%5E2-3n+-88+=+0\"$ ...factor completely\r
\n" ); document.write( "\n" ); document.write( " $\"n%5E2-11n%2B8n+-88+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28n%5E2-11n%29%2B%288n+-88%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"n%28n-11%29%2B8%28n+-11%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28n-11%29%28n%2B8%29+=+0\"$ \r
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\n" ); document.write( "\n" ); document.write( "solutions:
\n" ); document.write( "if $\"%28n%2B8%29+=+0\"$ => $\"n+=+-8\"$ cannot use this (side length must be positive number)\r
\n" ); document.write( "\n" ); document.write( "if $\"%28n-11%29=0\"$ => $\"n+=+11\"$ \r
\n" ); document.write( "\n" ); document.write( "so, the polygon with $\"44\"$ diagonals has $\"11\"$ sides\r
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