A) 7
B) 11
C) 8
D) none of these
Correct Answer: B
Solution :
Key Idea: If there are n sides of a polygon, then number of diagonals is \[^{n}{{C}_{2}}-n.\] Let the number of sides of a polygon be \[n\] \[\therefore \] \[{{\,}^{n}}{{C}_{2}}-n=44\] (given) \[\Rightarrow \]\[\frac{n(n-1)}{2}-n=44\] \[\Rightarrow \] \[n(n-3)=88\] \[\Rightarrow \] \[{{n}^{2}}-3n-88=0\] \[\Rightarrow \]\[{{n}^{2}}-11n+8n-88=0\] \[\Rightarrow \] \[(n-11)(n+8)=0\] \[\Rightarrow \] \[n=11,\]but \[n\ne -8\]
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