Correct Answer - Option 4 : 8.66 cm
Given-
Number of diagonals = 5
Length of each Side = √3 cm
Concept Used-
Number of diagonals of a regular polygon = n(n - 3)/2 [where n = Number of Sides of Polygon]
Perimeter of polygon = n × Length of each Side [where n = Number of Sides of Polygon]
Calculation-
Let the number of diagonals of the regular polygon = Number of Sides = n
According to Condition -
n(n - 3)/2 = n
⇒ (n - 3) = 2
⇒ n = 5
The polygon is pentagon.
∴ Perimeter of the polygon = 5 × √3
⇒ 8.66 cm