Question

In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3AB²= 4AD².

Answer 1

Given: ABC is an equilateral triangle and AD is the altitude on side BC

To Prove: 3AB²= 4AD²

In right triangle ∆ADB, using Pythagoras theorem

(Perpendicular)² + (Base)² = (Hypotenuse)²

⇒ AD² + BD² = AB²

⇒ 4AD² + BC² = 4AB²

⇒ 4AD² = 4AB² – BC²

⇒ 4AD² = 4AB² – AB² [∵ABC is an equilateral triangle]

⇒ 4AD² = 3AB²

Hence Proved