Question

If a polygon has $44$ diagonals, then the number of its side are:

• A. 7
• B. 11
• C. 8
• D. none of these

Answer 1

Answer: (B)

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 $