SOLUTION: If I know the polygon to get the number of diagonals I can use the formula n(n-3)/2 where n=the number of sides of the polygon. How can I find the polygon when I know the num

Algebra ->  Polygons -> SOLUTION: If I know the polygon to get the number of diagonals I can use the formula n(n-3)/2 where n=the number of sides of the polygon. How can I find the polygon when I know the num      Log On


   

Question 602117: If I know the polygon to get the number of diagonals I can use the formula n(n-3)/2 where n=the number of sides of the polygon. How can I find the polygon when I know the number of diagonals that can be drawn inside? ex. Which polygon has 20 diagonals that can be drawn inside? Is there a formula for this question?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of diagonals

The formula to find the number of diagonals 'd' is d=%28n%28n-3%29%29%2F2


Solve this for n to find the number of sides given the number of diagonals


d=%28n%28n-3%29%29%2F2

2d=n%28n-3%29

2d=n%5E2-3n

0=n%5E2-3n-2d

n%5E2-3n-2d=0

Now use the quadratic formula to solve for 'n'

n+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

n+=+%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%281%29%28-2d%29%29%29%2F%282%281%29%29

n+=+%283%2B-sqrt%289%2B8d%29%29%2F%282%29

n+=+%283%2Bsqrt%289%2B8d%29%29%2F%282%29 or n+=+%283-sqrt%289%2B8d%29%29%2F%282%29

So things are a bit uglier, but now you have a formula for 'n' given the number of diagonals 'd'.