SOLUTION: In which regular polygon is the number of diagonals equal to one and half time the number of sides?

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Question 633658: In which regular polygon is the number of diagonals equal to one and half time the number of sides?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A regular polygon with n sides would have n vertices.
From each vertex we can draw (n=3) diagonals to all the other vertex that are not adjacent.
Each diagonal, connecting two vertices, would be counted twice in the product n(n-3).
So the number of diagonals for a polygon with n sides would be n(n-3)/2.
If that is half the number of sides, we have
n(n-3)/2=n/2 --> n(n-3)=n --> n%5E2-3n=n --> n%5E2-4n=0 --> n%28n-4%29=0
The number of sides, n, cannot be zero, so highlight%28n=4%29.
The regular polygon is a highlight%28square%29.