Question

A convex polygon has 44 diagonals, find the number of sides of his this polygon.

Answer 1

No. of diagonals in a polygon of $n$ sides $=\frac{n(n-3)}{2}$

$\frac{n(n-3)}{2}=44$

$n(n-3)=88$

$n(n-3)=11(11-3)$

$\therefore n=11$

$\therefore$ No. of sides $=11.$