Recover Side Length from Area — Equilateral Triangle: The area of an equilateral triangle is 4√3 cm^2. Find the length of each side (in cm).

Introduction / Context:Equilateral triangle area depends solely on side length via a constant factor. Inverting the standard formula lets us find side length directly from a given area, reinforcing comfort with algebraic manipulation and radicals.

Given Data / Assumptions:

• Area A = 4√3 cm^2
• Formula: A = (√3/4) * a^2
• a is the side length in cm

Concept / Approach:Set 4√3 = (√3/4) * a^2 and solve for a^2 by isolating it. Cancel √3 on both sides to simplify early and avoid handling nested radicals later. Take the positive square root because side length is positive.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 4/√3 cm and √3/4 cm misapply inversion steps.
• 3 cm does not satisfy (√3/4)*9 = 2.25√3.
• 2√3 cm gives area (√3/4)*12 ≈ 3√3, not 4√3.

Common Pitfalls:

• Forgetting to multiply by 4/√3 to isolate a^2.
• Taking the square root prematurely before simplifying constants.

Final Answer:4 cm.