**Question:**

**A convex polygon has 44 diagonals. Find the number of its sides. [Hint: Polygon of n sides has (nC2 – n) number of diagonals.]**

**Solution:**

We know that,

nCr

$=\frac{n !}{r !(n-r) !}$

Let the number of sides the given polygon have = n

Now,

The number of line segments obtained by joining n vertices = nC2

So, number of diagonals of the polygon = nC2 – n = 44

$\frac{n(n-1)}{2}-n=44$

n2 – 3n – 88 = 0

(n – 11) (n + 8) = 0

n = 11 or n = – 8

The polygon has 11sides.