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Please help! A convex polygon has 65 diagonals. The number of its sides is equal to -

A convex polygon has 65 diagonals. The number of its sides is equal to - 

  • Option 1)

    13

  • Option 2)

    10

  • Option 3)

    22

  • Option 4)

    11

 
Answers (1)
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As learnt in concept

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

 

 If number of sides =n

Number of diagonals = \frac{n(n-3)}{2}= 65

n^{2}-3n-130=0

n^{2}-13n+10n-130=0

n= 13,-10

Thus n =13

 


Option 1)

13

Correct option

Option 2)

10

Incorrect option

Option 3)

22

Incorrect option

Option 4)

11

Incorrect option

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