Question

In an equilateral triangle ABC if AD ⊥ BC, then

Options

• 5AB² = 4AD²

• 3AB² = 4AD²

• 4AB² = 3AD²

• 2AB² = 3AD²

Answer 1

∆ABC is an equilateral triangle and `AD ⊥ BC`.

In ∆ABD, applying Pythagoras theorem, we get

`AB^2=AD^2+BD^2`

`AB^2=AD^2+(1/2BC)^2(∵BD=1/2BC)`

`AB^2=AD^2+(1/2AB)^2(∵ AB=BC)`

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

`3AB^2=4AD^2`

We got the result as `b`.