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# A polygon has 44 diagonals. The no. of sides of the polygon = ?

$\begin{array}{1 1} 8 \\ 11 \\ 12 \\ 13 \end{array}$

Let the polygon be n sided.
The no. of lines that can be drawn using the vertices = $^nC_2$
This includes n lines which are sides.
$\therefore$ No. of diagonals = $^nC_2-n=\large\frac{n(n-1)}{2}$$-n=44\:(given)$
$\Rightarrow\:n^2--3n-88=0$
$\Rightarrow\:(n+8)(n-11)=0$
$\Rightarrow\:n=11\:\:or\:\:-8\:(not\:possible.)$
$\therefore\:n=11$