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

Options

A. 7
B. 8
C. 9
D. 11

Answer

D

Explanation

Let n be the number of sides of the polygon, then number of diagonals = `""^nC_2 - n`
According to the question, `""^nC_2 - n = 44 `
or, `(n(n -1))/(2) - n = 44`
or `n^2 - n - 2n = 88`
or `n^2 - 3n - 88 = 0`
or,`(n - 11)(n + 8) = 0`
or `n = 11 " or " n = -8 " " [because n != -8]`
`therefore n = -8` is discarded.
So, `n = 11`.
Therefore, the number of sides of the polygon = 11.
Note : Remember that number of diagonals of the polygon `= ""^nC_2- n`
or `(n(n -3))/(2)`