SOLUTION: A polygon of n side has {{{n(n-3)/2}}} diagonals. How many sides has a polygon with 77 diagonals? The sum of first n positive integers is {{{S=n(n+1)/2}}}. How many consecutive

Question 411529: A polygon of n side has diagonals. How many sides has a polygon with 77 diagonals?
The sum of first n positive integers is . How many consecutive integers, starting with 1, are required to add up to 66?

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
a ploygon of n side has(n-3) diagonals. how many sides has a polygon with 77 diagonals.
the sum of first integers n is s=(n+1). find how many integers are required to add up to 66


Both those formulas are wrong. A polygon with n sides has  diagonals,
not n-3. The sum of the first n integers n is , not n+1. 

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I will answer using the correct formulas, not the ones given.

How many sides has a polygon with 77 diagonals?







n+11=0          n-14=0
   n= -11          n=14

We discard the negative answer.  The correct solution is a 14-sided
polygon.

-------------------------------------

How many integers are required to add up to 66?


 




n-11=0       n+12=0
   n=11        n=-12

We discard the negative answer.  The correct solution is the first
11 integers:

1+2+3+4+5+6+7+8+9+10+11=66

Edwin

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