Equilateral triangle — Find the altitude when the side is 2√3 cm.

Introduction / Context:In an equilateral triangle of side a, the altitude (height) is a * (√3/2). This comes from splitting the triangle into two 30-60-90 right triangles, where the height is the longer leg.

Given Data / Assumptions:

• a = 2√3 cm
• Altitude h = (√3/2) * a

Concept / Approach:Apply the standard altitude formula for equilateral triangles directly.

Step-by-Step Solution:h = (√3/2) * (2√3) = (2 * 3) / 2 = 3 cm

Verification / Alternative check:Compute area via (√3/4)a^2 = (√3/4)*(12) = 3√3; also via (1/2) * base * height = (1/2)*(2√3)*3 = 3√3, consistent.

Why Other Options Are Wrong:√3/2 cm and √3/4 are fragments of the formula; 1/2 cm is unrelated; 2 cm is not consistent with the 30-60-90 ratios.

Common Pitfalls:Forgetting to multiply the side by √3/2; confusing altitude with median length without evaluating the factor correctly.

Final Answer:3 cm