Question

A polygon has 44 diagonals, then the number of its side are

• A. 11
• B. 9
• C. 7
• D. 5

Answer 1

The correct option is A 11

At the number of sides be n.

${}^n{C}_2-n=44,n>0\Rightarrow \frac{n(n-1)}{2}-n=44$

$\Rightarrow n^2-3n-88=0$

$\Rightarrow n^2-11n+8n-88=0$

$\Rightarrow n(n-11)+8(n-11)=0$

$\Rightarrow (n-11)(n+8)=0$

$\Rightarrow n=11$