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.