If a polygon of n sides has 275 diagonals, then n is equal to

Step-by-step solution

The number of diagonals in a polygon of n sides is given by the formula D = n(n - 3) 2 . Given D = 275 , we have the equation: n(n - 3) 2 = 275 n(n - 3) = 550 n^2 - 3n - 550 = 0 Solving the quadratic equation using the quadratic formula n = -b b^2 - 4ac 2a : n = 3 (-3)^2 - 4(1)(-550) 2(1) n = 3 9 + 2200 2 n = 3 2209 2 n = 3 47 2 Since n must be positive, we take the positive root: n = 3 + 47 2 = 50 2 = 25 Answer: 25