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

Options

A. 11
B. 12
C. 13
D. 15

Answer

A

Explanation

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