Question

If ∆ABC is an equilateral triangle such that AD ⊥ BC, then AD² =

 

Options

• \[\frac{3}{2} {DC}^2\]

• 2 DC²

• 3 CD²

• 4 DC²

Answer 1

Given: In an equilateral ΔABC, `AD ⊥ BC`.

Since `AD ⊥ BC`., BD = CD = \[\frac{BC}{2}\]

Applying Pythagoras theorem,

In ΔADC

`AC^2+AD^2+DC^2`

`BC^2=AD^2+DC^2`(Since AC=BC)

`(2DC)^2=AD^2+DC^2`(Since BC=2DC)

`4DC^2=AD^2+DC^2`

`3DC^2=AD^2`

`3DC^2=AD^2`

We got the result as `c`