Question

In an equilateral triangle ABC, if AD ⊥ BC then which of the following is true?

Options

• 2AB² = 3AD²

• 4AB² = 3AD²

• 3AB² = 4AD²

• 3AB² = 2AD²

Answer 1

3AB² = 4AD²

Explanation:

AB² = BD² + AD² 

= `(1/2 AB)^2 + AD^2`

= `1/4 AB^2 + AD^2`

⇒ `3/4 AB^2 = AD^2`

 ⇒ 3AB² = 4AD²