Question

1)A polygon has 27 diagonals. How many sides does it have?

Answer 1

The formula for the no. of diagonals of a ’n' sided polygon is n(n-3)/2 .

It works for triangle (0 diagonals) , quadrilateral (2 diagonals) , pentagon (5 diagonals) and for every another polygon.

Let's come to the problem.

No. Of diagonals = n(n-3)/2 = 27

n(n-3) = 54

n^2 - 3n -54 = 0

n^2 - 9n + 6n - 54 = 0

n(n-9) + 6(n-9) = 0

(n-9)(n+6) = 0

n = 9, -6

(excluding -6)

n = 9

The polygon has 9 sides.

It is a Nonagon.