Question

a convex polygon has 44 diagonals. the number of its side is ?

Answer 1

Polygon with n sides has n(n-3)/2 diagonals. for ex, rectangle has 2 diagonals
polygon with 44 diagonals:
44 = n(n-3)/2
solving for n
n^2-3n -88 = 0
factoring
(n-11)(n+8) = 0
(n+8) = 0
n = -8 cannot use this
(n-11)=0
n = 11
Polygon has 11 sides
checking our answer
11*8/2 = 44 diagonals