SOLUTION: Solve the problem. If a polygon, of n sides has 1/2n(n - 3) diagonals, how many sides will a polygon with 779 diagonals have?

Algebra ->  Polygons -> SOLUTION: Solve the problem. If a polygon, of n sides has 1/2n(n - 3) diagonals, how many sides will a polygon with 779 diagonals have?      Log On


   

Question 1048508: Solve the problem.
If a polygon, of n sides has 1/2n(n - 3) diagonals, how many sides will a polygon with 779 diagonals have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

expr%281%2F2%29n%28n+-+3%29%22%22=%22%22779

Multiply through by 2:

n%28n+-+3%29%22%22=%22%221558

n%5E2+-+3n%29%22%22=%22%221558

n%5E2+-+3n-1558%29%22%22=%22%220

%28n-41%29%28n%2B38%29%22%22=%22%220

n-41%22%22=%22%220; n%2B38%22%22=%22%220

n%22%22=%22%2241;   n%22%22=%22%22-38

A polygon cannot have a negative number of sides, so

n = 41.

Edwin