Question

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

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

Answer 1

The correct option is B $11$

The formula for number of diagnols of a $n-$sided polygon is $\frac{n(n-3)}{2}$

Here number of diagnols$=$$44$

$\Rightarrow$ $n(n-3)=88$

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

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

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

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

$\Rightarrow$$n=11$ or $n=-8$

Number of Sides cannot be negative.$\therefore n=11$

$\therefore$ Option B is correct