Question

A polygon has 44 diagonals if n denotes the number of vertices of polygons find the value of and hence find the number of triangles that can be formed by joining the same points

Answer 1

Answer:

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