A polygon has 54 diagonals. The number of sides of this polygon is
A polygon has 54 diagonals. The number of sides of this polygon is
12
15
16
9
Solution
Let number of sides of the polygon is \(n\), then number of diagonals is
\(\begin{aligned}
\frac{n(n-3)}{2} & =54 \quad \text{(given)} \\
\Rightarrow \quad n(n-3) & =108 \quad \Rightarrow n=12
\end{aligned}\)