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The number of diagonals of a regular polygon is equal to the number of its sides and length of each Side is √3 cm. Find the perimeter of the polygon.
1. 5√2 cm
2. 4.33 cm
3. 17.32 cm
4. 8.66 cm

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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

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