Equilateral triangle from area — find perimeter: An equilateral triangle has area 3√3 sq cm. Find its perimeter.

Introduction / Context:The area of an equilateral triangle in terms of side a is A = (sqrt(3)/4) * a^2. From area we can get side, then multiply by 3 for perimeter.

Given Data / Assumptions:Area A = 3*sqrt(3) sq cm.

Concept / Approach:Set (sqrt(3)/4)*a^2 = 3*sqrt(3) and solve for a, then perimeter P = 3a.

Step-by-Step Solution:(sqrt(3)/4)*a^2 = 3*sqrt(3)Divide both sides by sqrt(3): a^2 / 4 = 3 ⇒ a^2 = 12 ⇒ a = 2*sqrt(3)Perimeter P = 3a = 6*sqrt(3) cm

Verification / Alternative check:Plugging back: (sqrt(3)/4)*12 = 3*sqrt(3) ✓

Why Other Options Are Wrong:They do not align with the derived side length.

Common Pitfalls:Misapplying the area formula or taking the square root incorrectly.

Final Answer:6√3 cm