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Question
A polygon has 1325 diagonals. How many vertices does it have?
 Question Submitted By :: Guest
I also faced this Question!!     Rank Answer Posted By  
 
  Re: A polygon has 1325 diagonals. How many vertices does it have?
Answer
# 1
The formula to find number of diagonals (D) given total
number of vertices or sides (N) is

                 N * (N - 3)    

           D  =  -----------       

                     2

Using the formula, we get 

1325 * 2 = N * (N - 3) 

N2 - 3N - 2650 = 0 

Solving the quadratic equation, we get N = 53 or -50 

It is obvious that answer is 53 as number of vertices can
not be negative. 

Alternatively, you can derive the formula as triange has 0
diagonals, quadrangel has 2, pentagon  

has 5, hexagon has 9 and so on...... 

Hence the series is 0, 0, 0, 2, 5, 9, 14, ........ (as
diagram with 1,2 or 3 vertices will have 0  

diagonals). 

Using the series one can arrive to the formula given above.
 
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