A number of diagonal is equal to the perimeter of n sided polygon. If each side is 2 cm long then n will be:

Formula used:

The number of diagonals that can be drawn by joining the angular points of a polygon having n sides is given by:

 \({\;^n}{C_2} - n = \frac{{n × \left( {n - 3} \right)}}{2}\)

The perimeter of polygon = n × (side of a polygon)

Calculation:

Given that,

Length of the side of polygon = 2 cm

According to the question,

The number of diagonal is equal to the perimeter of n sided polygon.

⇒ \(\frac{{n × \left( {n - 3} \right)}}{2} = n\times 2\)

⇒ n - 3 = 4

⇒ n = 7