Question

The polygon has 44 diagonals then the number of its side are

Answer 1

Note -- Polygon with 'n' number of sides has { [n(n-3)] / 2} number of diagonals. For e.g. A rectangle has 2 diagonals and 4 sides.

A polygon with 44 diagonals:

44 = [n(n-3)] / 2

Solving the following quadratic equation for 'n' :--

n^2-3n -88 = 0

On factorising it.....

(n-11)(n+8) = 0

=> (n+8) = 0

n = - 8
(We can't consider this value as we know that a polygon can never have 'negative' value of its sides.)

=> (n-11)=0

n = 11

Thus, the polygon has 11 sides .


__________________
Checking our answer:

11*8/2 = 44 diagonals

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