Question

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

Answer 1

`(n(n-3))/(2)=d \ \ \ \ \ \text{[n - number of sides, d - number of diagonals] } \\ \\ (n(n-3))/(2)=27 \\ n(n-3)=27*2 \\ n^2-3n = 54 \\ n^2-3n-54=0 \\ discriminant=(-3)^2-4*1*(-54)=225 \\ n_1= (3- √(225) )/(2)= (3-15)/(2) = -6 \ \ \ \O \\ n_2= (3+ √(225) )/(2)= (3+15)/(2) = 9`

The polygon has 9 sides.