Equilateral triangle area given — find side length: The area of an equilateral triangle is (√243)/4 sq cm. Find the side length (in cm).

Introduction / Context:Area of an equilateral triangle is (sqrt(3)/4)*a^2. Here the area is expressed as (sqrt(243))/4. Recognize that sqrt(243) = 9*sqrt(3) to simplify.

Given Data / Assumptions:A = (sqrt(243))/4 = (9*sqrt(3))/4 sq cm.

Concept / Approach:Set (sqrt(3)/4)*a^2 = (9*sqrt(3))/4. Cancel sqrt(3)/4 on both sides to get a^2 = 9.

Step-by-Step Solution:(sqrt(3)/4)*a^2 = (9*sqrt(3))/4a^2 = 9 ⇒ a = 3 cm

Verification / Alternative check:Plug back: (sqrt(3)/4)*9 = (9*sqrt(3))/4 ✓.

Why Other Options Are Wrong:3√3 cm and √3 cm are misinterpretations; 9 cm corresponds to a^2, not a.

Common Pitfalls:Not simplifying sqrt(243) or forgetting to take the principal square root.

Final Answer:3 cm