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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 Solution | Comment 2 of 16 |
Answer: it has 53 vertices.

Explanation:

If a polygon has N vertices, then every vertex has (N-3) vertices that are nonadjacent, with a diagonal between them. Since every diagonal connects 2 vertices, division by 2 will avoid counting diagonals twice.

If N(N-3)/2 = 1325,

then N=53
Edited on February 1, 2004, 10:08 am
  Posted by Penny on 2004-01-31 10:43:08
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