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

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bharat bajaj · Answer

Let the polygon has n sides .Then it will have n vertices. By joining any two vertices, we will get a side or a diagonal. No. of line segments obtained by joining n vertices = N C 2 Out of these n line segments are sides of the polygon. So, no. of diagonals of the polygon = n C 2 - n Given, n C 2 - n = 44 n (n - 1) / 2 - n = 44 n (n - 3) / 2 = 44 n 2 - 3n - 88 = 0 (n - 11) (n + 8) = 0 n = 11 or n = - 8 Since n cannot be negative, n = 11 The polygon has 11 sides. THanks Bharat Bajaj askiitians faculty IIT Delhi

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

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

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