SOLUTION: A regular polygon has twelve diagonals. Find the number of sides?

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Question 1076154: A regular polygon has twelve diagonals. Find the number of sides?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The number of diagonals of a convex n-sided polygon is %28n%2A%28n-3%29%29%2F2.


To answer the question, you need to solve the equation


%28n%2A%28n-3%29%29%2F2 = 12.


--->  n*(n-3) = 24 --->  n^2 - 3n - 24 = 0  --->    


--->  there is NO integer solution.


--->  Your formulation is wrong. There is no such a polygon.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try drawing the first few simple regular polygons and draw and count the number of diagonals of each.

n number of sides
d number of diagonals 

n        d
3        0
4        2
5        5
6        9
7       14

NO such regular polygon will have 12 diagonals.
No convex polygon will have 12 diagonals.