Question

A regular polygon with n sides has n(n-3)/2 diagonals. Find the number of sides of a regular polygon that has 44 diagonals.

Answer 1

`(n(n-3))/(2)=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8`

Therefore, the number of sides is 11.