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Diagonals Of A Polygon (Posted on 2004-01-31) Difficulty: 2 of 5
A polygon has 1325 diagonals. How many vertices does it have?

No Solution Yet Submitted by Ravi Raja    
Rating: 2.4167 (12 votes)

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Solution Kind of simple... | Comment 13 of 16 |
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
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