Question

A polygon has 44 44 diagonals, the number of its sides are

Answer 1

11

A polygon of n sides has n vertices. By joining any two vertices of a polygon, we obtain either a side or a diagonal of the polygon.

A number of line segments obtained by joining the vertices of a n sided polygon taken two at a time = Number of ways of selecting 2 out of n.

= n^C2

= n ( n − 1 ) /2

Out of these lines, n lines are the sides of the polygon, sides can’t be diagonals.

∴ Number of diagonals of the polygon =

n ( n − 1 )/ 2 - n = n ( n − 3 )/ 2

Given that a polygon has 44 diagonals.

Let n be the number of sides of the polygon.

n ( n − 3 ) /2 = 44

⇒ n(n – 3) = 88

⇒ n^2 – 3n – 88 = 0

⇒ (n + 8) (n – 11)

⇒ n = -8 (or) n = 11

n cannot be negative.

∴ n = 11 is number of sides of polygon