Question

A polygon has $44$ diagonals. The number of its sides is

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

Answer: (B)

$11$

Let the sides of a polygon be $n$.
$\therefore {}^n{C}_2-n=44$
$\Rightarrow \frac{n(n-1)}{2}-n=44$
$\Rightarrow \frac{n(n-3)}{2}=44$
$\Rightarrow n(n-3)=11\times 8$
$\Rightarrow n=11$