Question

A polygon has $44$ diagonals, then the number of its sides is:

• A. $11$
• B. $9$
• C. $7$
• D. $5$

Answer 1

The correct option is A $11$

Let the number of sides be $n$
Therefore, ${}^n{C}_2-n=44,n>0$
$\Rightarrow \frac{n(n-1)}{2}-n=44$
$\Rightarrow n^2-3n-88=0$
$\Rightarrow n^2-11n+8n-88=0$
$\Rightarrow n(n-11)+8(n-11)=0$
$\Rightarrow (n-11)(n+8)=0$
$\Rightarrow n=11$