Question

A polygon has 27 diagonals. How many
Sides does it have?​

Answer 1

Answer:

The sides of polygon is 9.

Answer 2

Answer:

We know that,

Number of diagonals of a polygon =   n(n−3)/2

​  

According to the question,

 

n(n−3)/2 = 27

n(n - 3) = 54  

n2 - 3n - 54 = 0

n2 9n + 6n - 54 = 0

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

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

n = 9, - 6 (Neglecting negative value)

n = 9  

Hence, sides of polygon are 9.