Question

A polygon has 44 diagonals, then the number of its sides are ?

Answer 1

Answer:

11 Sides

Step-by-step explanation:

If you are talking about an n-sided convex polygon, then its number of diagonals are given by nC2 - n; and if  

nC2 - n = 44 (given), then  

½ n (n - 1) - n = 44  

n^2 - n - 2 n = 88  

n^2 - 3 n - 88 = 0  

Solving the quadratic, we have  

n^2 - 11 n + 8 n - 88 = 0  

(n - 11) (n + 8) = 0  

Since, n = -8 is not applicable, hence the polygon in question must have 11 number of sides to it.