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Find the no. of sides of a polygon in which the no. of diagonals are 27 ?
1. 6
2. 8
3. 9
4. 11

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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.

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