SOLUTION: If a polygon has 44 diagonals then the no. of its sides is ?

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Question 996978: If a polygon has 44 diagonals then the no. of its sides is ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

recall:
Polygon with n sides has n%28n-3%29%2F2 diagonals
so, the polygon with 44 diagonals will have:
44+=+n%28n-3%29%2F2...solve for n
88+=+n%28n-3%29
88+=+n%5E2-3n
n%5E2-3n+-88+=+0...factor completely
n%5E2-11n%2B8n+-88+=+0
%28n%5E2-11n%29%2B%288n+-88%29+=+0
n%28n-11%29%2B8%28n+-11%29+=+0
%28n-11%29%28n%2B8%29+=+0

solutions:
if %28n%2B8%29+=+0=>n+=+-8 cannot use this (side length must be positive number)
if %28n-11%29=0 =>n+=+11
so, the polygon with 44 diagonals has 11 sides