A convex polygon has 44 diagonals. The number of its sides is

The number of diagonals in a polygon can be calculated using the formula n(n-3)/2, where n is the number of sides.

So, if a polygon has 44 diagonals, we can set up the equation:

n(n-3)/2 = 44

Solving for n, we get:

n^2 - 3n - 88 = 0

This is a quadratic equation, and we can solve it using the quadratic formula:

n = [3 ± sqrt((3)^2 - 41(-88))]/(2*1) n = [3 ± sqrt(9 + 352)]/2 n = [3 ± sqrt(361)]/2 n = [3 ± 19]/2

We get two solutions, n = 11 and n = -16. However, the number of sides of a polygon cannot be negative, so we discard -16.

Therefore, the polygon has 11 sides.