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

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A polygon has 44 diagonals. The number of its sides are
A. 11
B. 10
C. 8
D. 7
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Correct Answer - A
No. of diagonals in a polygen `= .^(n)C_(2) - n`
`rArr 44 = .^(n)C_(2) - n`
`rArr 44 = (n!)/(2!(n-2)!) - n`
`rArr 44 = (n(n-1))/(2) -n`
`rArr 44= (n(n-3))/(2)`
`rArr n^(2) -3n - 88 = 0`
`rArr (n-11) (n +8) = 0`
`n != -8`
`n = 11`
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