Correct Answer - Option 3 : 7
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