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  • Please help! 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 :

 

  • Option 1)

    10

  • Option 2)

    12

  • Option 3)

    9

  • Option 4)

    6

 

Answers (2)

best_answer

As we have learned

Geometrical Permutations -

The number of diagonals of n sided convex polygon is ^{n}c_{2}-n=\frac{n(n-3)}{2}.

- wherein

Where n > 3

 

 no. of diagonals = _{2}^{n}\textrm{C} -n = 54

\Rightarrow \frac{n(n-1)}{2}-2=54

\Rightarrow n^2-n-2n-108=0

\Rightarrow n^2-3n-108=0

\Rightarrow n^2-12n+9n-108=0

\Rightarrow (n-12)(n+9)=0

\Rightarrow n= 12

 

 

 

 

 


Option 1)

10

Option 2)

12

Option 3)

9

Option 4)

6

Posted by

Himanshu

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No.of diagonals=n(n-3)/2

54=n (n-3)/2

So n=12

Posted by

ABHOUMA S SUNIL

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