Question

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

Answer 1

IN THE TRIANGLE AD IS ALTITUDE .
AD²+DB²=AB²
⇒AD²+(1/2 * BC)²=AB²
⇒AD²+BC²/4=AB²
⇒4AD²+BC²=4AB²
⇒4AD²=4AB²-BC²
⇒4AD²=4AB²-AB²
⇒4AD²=3AB²
⇒AD²=3/4*AB²

Answer 2

see the attachment for right proof.