The number of diagonals of any (convex) polygon is  ,

where "n" is the number of sides (vertices).


So, they ask you to find "n" from the equation


     = 44.


Simplify and solve for "n" :


    n*(n-3) = 44*2 = 88

    n^2 - 3n - 88 = 0

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


Of the two roots,  n= 11  and  n= -8,  only positive root n= 11 is meaningful solution to the problem.


ANSWER.  n = 11.  The number of sides and vertices is 11.