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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