A polygon has 1325 diagonals. How many vertices does it have?

The formula for diagonals is d = n(n-3)/2, where d is the # of diagonals, and n is the # of sides (or vertices). Just solve for n...

2d=n(n-3)
2d=n^2-3n
2650=n^2-3n
n^2-3n-2650=0
---Solve w/ the quadratic formula--- (I'm probably doing this more complicated than necessary, but I'm too tired to find a better way...)
And, since you can only use the positive root,
the figure as 53 vertices.

Posted by Matt on 2004-12-08 03:26:27