Area Of Equilateral Triangle Is Numerically Equal To Its Perimeter

The area of an equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2 decimal places.

Answers:

Let each side of the equilateral triangle = x

∴   Its area = (√3/4) x2

Area perimeter = 3x

By the given condition = (√3/4) x= 3x

x2 = 3x × (4/√3)

x2 = (3x × 4 × √3)/ (√3 × √3) = (3x × 4 × √3)/3 = 4x√3

⇒ x2 = √3 (4x) ⇒ x = 4√3  [∵ x ≠ 0]

∴ Perimeter = 12√3 units

= 12 (1.732) = 20. 784 = 20. 78 units