Question

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

Answer 1

Let there be n sides of the polygon. We know that the number of diagonals of n sided polygon is $\frac{n(n-3)}{2}$.

Therefore,

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

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

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

$n=11$

Hence, there are 11 sides of the polygon.