Question

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

A. 7 

B. 8 

C. 9 

D. 12

Answer 1

Let x be sides of polygon. 

No. of Diagonals = 27 

According to formula,

No. of Diagonals = \(n\times\frac{n\,-\,3}{2}\)

\(27=n\times\frac{n\,-\,3}{2}\)

n (n - 3) = 54 

n² – 3n – 54 = 0 

(n + 6) (n - 9) = 0 

n = - 6 or 9 

Since, no of sides can’t be negative. 

So, No. of sides of polygon will be 9.