In an equilateral △ABC, let AD ⟂ BC. Which relation between AB and AD is true?

Introduction / Context:In an equilateral triangle of side s, the altitude AD has a standard length related to s. Substituting that value yields identities among AB and AD.

Given Data / Assumptions:

• AB = s.
• Altitude AD = (√3/2)s.

Concept / Approach:Compute AB² and AD², then test which given identity holds exactly without approximation.

Step-by-Step Solution:

Verification / Alternative check:Other listed relations evaluate to unequal expressions when substituting AB² and AD² as above.

Why Other Options Are Wrong:They swap coefficients incorrectly; only the 3:4 relation matches altitude length in an equilateral triangle.

Common Pitfalls:Using median length s/2 or height s*(√3/3) (which is the inradius) instead of the altitude length (√3/2)s.

Final Answer:3AB2 = 4AD2