Correct Answer - Option 3 : 9

**Given:**

Number of Diagonals = 27

**Formula used:**

No. of diagonals = n × (n - 3)/2

**Calculations:**

⇒ n × (n - 3)/2 = 27

⇒ n × (n - 3) = 54

⇒ n^{2} - 3n = 54

⇒ n^{2} - 3n - 54 = 0

⇒ n^{2} - 9n + 6n - 54 = 0

⇒ n(n - 9) + 6(n - 9) = 0

⇒ (n - 9) (n + 6) = 0

⇒ n = 9 (Sides are never negative i.e n ≠ -6)

**∴ Sides of polygons with 27 diagonals are 9.**