Let ∆ABC be the given equilateral triangle.
∴ ∠B = 60° [Angle of an equilateral triangle]
AD ⊥ BC, B – D – C.
In ∆ABD, ∠B = 60°, ∠ADB = 90°
∴ ∠BAD = 30° [Remaining angle of a triangle]
∴ ∆ABD is a 30° – 60° – 90° triangle.
∴ Side of equilateral triangle = 2 cm
Perimeter of ∆ABC = 3 × side
= 3 × AB
= 3 × 2
= 6 cm
∴ The length of the side and perimeter of the equilateral triangle are 2 cm and 6 cm respectively.