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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

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
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 =NC2
Out of these n line segments aresidesof the polygon.
So, no. of diagonals of the polygon =nC2- n
Given,nC2- n = 44
n (n - 1) / 2 - n = 44
n (n - 3) / 2 = 44
n2- 3n - 88 = 0
(n - 11) (n + 8) = 0
n = 11 or n = - 8
Since n cannot be negative, n = 11
The polygon has 11sides.
THanks
Bharat Bajaj
askiitians faculty
IIT Delhi

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