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A polygon has 44 diagonals. The number of its sides is
Let the polygon has nsides.Then it will have n vertices.Byjoiningany two vertices, we will get a side or a diagonal.No. of line segments obtained byjoiningn vertices =NC2Out of these n line segments aresidesof the polygon.So, no. of diagonals of the polygon =nC2- nGiven,nC2- n = 44n (n - 1) / 2 - n = 44n (n - 3) / 2 = 44n2- 3n - 88 = 0(n - 11) (n + 8) = 0n = 11 or n = - 8Since n cannot be negative, n = 11The polygon has 11sides.THanksBharat Bajajaskiitians facultyIIT Delhi
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