Question

A polygon of n sides has n(n-3) /2 diagonals. If a polygon has 9diagonal, find the no. Of sides of the polygon.

Answer 1

Answer:

# sides = 6

Step-by-step explanation:

# diagonals = 9

=>  n ( n - 3 ) / 2 = 9

=>  n ( n - 3 ) = 18

=>  n² - 3 n - 18 = 0

=>  ( n - 6 ) ( n + 3 ) = 0

=>  n = -3 or n = 6.

Since the number of sides must be positive, we conclude n = 6.