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
⇒ n2 - 3n = 54
⇒ n2 - 3n - 54 = 0
⇒ n2 - 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.