CMAT 2014 Solved Question Paper

We know that, number of diagonals in polygon = $\frac{\mathit{n}\left(\mathit{n}-3\right)}{2}$
⇒ 54 = $\frac{\mathit{n}\left(\mathit{n}-3\right)}{2}$
n(n - 3) = 108 ⇒ ${\mathit{n}}^2$ - 3n - 108 = 0
${\mathit{n}}^2$ - 12n + 9n - 108 = 0
n(n -12) + 9(n -12)= 0
(n-12)(n+ 9) = 0 ⇒ n = 12 , -9
∴ Total number of sides = 12