Find The Number of Sides of Polygon ?

The polygon has 44 diagonals. The number of its sides is

  1. 11
  2. 10
  3. 8
  4. 7
Anurag Mishra Professor Asked on 30th September 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 11

    Explanation:-
    Formula –
    The number of diagonals in a polygon = [n(n – 3)]/2
    Where, n = number of sides of polygon

    Then, 44 = n (n – 3)/2
    44 = [ n^2 – 3 n]/2
    by  cross multiplication,
    2 x 44 = n^2 – 3 n
    n^2 – 3 n – 88 = 0
    n^2 – 11 n + 8 n – 88 = 0
    n (n – 11)  + 8 (n – 11) = 0
    n – 11 = 0
    n = 11

    Then, the number of sides of the polygon is 11.

    Hence, the answer is (1) 11.

    Anurag Mishra Professor Answered on 3rd October 2015.
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