If a polygon has 14 diagonals, then the number of its sides are

Solution:

Let n be the number of diagonals of a polygon .Then

$\begin{array}{l}{ }^{\mathrm{n}}{\mathrm{C}}_2-\mathrm{n}=44\\ \Rightarrow \frac{\mathrm{n}(\mathrm{n}-1)}{2}-\mathrm{n}=44\\ \Rightarrow {\mathrm{n}}^2-3\mathrm{n}-88=0\\ \Rightarrow \mathrm{n}=-8 \mathrm{or} 11\\ \mathrm{n}=11\end{array}$