Q. 134.2( 19 Votes )

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Answer :

No. of diagonals =

n(n - 3) = 2 × 65


n2 - 3n = 130


n2 - 3n - 130 = 0


Performing factorization we get:


n2 - 13n + 10n - 130 = 0


n(n - 13) + 10(n - 13) = 0


(n + 10)(n - 13) = 0


n = 13, - 10


Since no. of sides cannot be negative so


No. of Sides = 13


When No. of Diagonals is 50


n(n - 3) = 50 × 2


n2 - 3n - 150 = 0


Discriminant = (9 - 4 × 1 × ( - 150)) = 609


Since 609 is not a perfect square so n can never be a whole number.


Hence 50 diagonals are not possible


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