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 $n\ne -8$