Question

A polygon has $44$ diagonals. Find the number of sides of the polygon

Answer 1

Solution:

Diagonals of $n$ sides of a polygon $=\frac{n(n-3)}{2}$

$44=\frac{n^2-3n}{2}$

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

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

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

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

$n=11$ or $n=-8$

$n$ can't be negative so, $n=11$

$\therefore$ number of sides $=11$