Question

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

Answer 1

polygon 27 diagonal nine sides

Answer 2

Hello,

A polygone with n sides has n*(n-3)/2 diagonals

$n\geq0\\ \dfrac{n*(n-3)}{2} =27\\ \Rightarrow\ n^2-3n=54\\ \Rightarrow\ n^2-3n-54=0\\ \Rightarrow\ n^2-9n+6n-54=0\\ \Rightarrow\ n(n-9)+6(n-9)=0\\ \Rightarrow\ (n-9)(n+6)=0\\ \Rightarrow\ n=9\ or\n=-6$

Number of sides: 9