A polygon has 44 diagonals. The number of its sides areA. 11B. 12C. 13

1.	A polygon has 44 diagonals. The number of its sides areA. 11B. 12C. 13D. 15
Answer» Correct Answer - A Let the convex polygon has n sides. `therefore` Number of diagonals `= ""^(n)C_(2) - n` According to the question, `""^(n)C_(2) - n = 44` `(n"!")/(2"!"(n -2)"!") - n = 44` `rArr` `(n(n-1))/(2) - n = 44` `rArr` `n[((n-1))/(2)-1]=44 " "rArr n((n-1-2)/(2)) = 44` `rArr` `n(n-3) = 44 xx 2 " "rArr n(n-3) = 88` `rArr` `n^(2) - 3n - 88 = 0 " "rArr (n-11) (n+8) = 0` `rArr` `n = 11, - 8" "` `[because n = -8]` `therefore` n = 11

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A polygon has 44 diagonals. The number of its sides areA. 11B. 12C. 13D. 15

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