document.write( "Question 633658: In which regular polygon is the number of diagonals equal to one and half time the number of sides? \n" ); document.write( "

Algebra.Com's Answer #399076 by KMST(5328) $\"\"$ $\"About$

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A regular polygon with n sides would have n vertices.
\n" ); document.write( "From each vertex we can draw (n=3) diagonals to all the other vertex that are not adjacent.
\n" ); document.write( "Each diagonal, connecting two vertices, would be counted twice in the product n(n-3).
\n" ); document.write( "So the number of diagonals for a polygon with n sides would be n(n-3)/2.
\n" ); document.write( "If that is half the number of sides, we have
\n" ); document.write( "n(n-3)/2=n/2 --> n(n-3)=n --> $\"n%5E2-3n=n\"$ --> $\"n%5E2-4n=0\"$ --> $\"n%28n-4%29=0\"$
\n" ); document.write( "The number of sides, n, cannot be zero, so $\"highlight%28n=4%29\"$ .
\n" ); document.write( "The regular polygon is a $\"highlight%28square%29\"$ . \n" ); document.write( "

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