Question

A polygon has 119 diagonals find its number of sides

Answer 1

For find the sides or Diagonal of polygon formula is-

d = s(s-3)/2

2d = s(s-3)

s2 -3s -2d = 0 (this is the standard form of a quadratic equation. You use the quadratic formula to solve it.)

[S= -b±√b^2-4ac/2a]

s = (3 ±√(32 - 4*(1)(-2d)))/(2*(1))

s = (3 +√(9+8d))/2

probably only the positive root is useful

For d = 119, this is

s = (3 +√(9+8*119))/2 = (3+√961)/2 = (3+31)/2 = 34/2 = 17

Your polygon has 17 sides.