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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 My Solution | Comment 10 of 16 |
The formula for number of diagonals in a polygon is
n(n-3)/2 where n is the number of sides.
Since here, we are given the number of diagonals,
n(n-3)/2=1325
n*n - 3n = 2650
n*n - 3n - 2650 = 0,
we get n as 53. Hence the number of sides is 53, and since the number of sides = number of vertices, the number of vertices is 53.
Thanks

  Posted by shawn on 2004-02-15 22:19:54
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