If in a regular polygon the number of diagonals is 54 , then the number of sides of this polygon is:

If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is:
  1. 12
  2. 10
  3. 6
  4. 9

Solution

Number of diagonals of an ′n′ sided polygon is

 nC2 -n=54

nn-11.2-n=54

n2-n2-n=54

n2 -3n = 108

n2-3n-108=0

n-12n+9=0

n=12

Asked in: JEE Main 2015 (11 Apr Online)

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