In an equilateral triangle ABC if , then

Given in equilateral triangle ABC if AD ⊥ BC.

We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Now, in right triangle ABD,

⇒ AB² = AD² + BD²

⇒ AB² = AD² + ( � BC)² [∵ BD = �BC]

⇒ AB² = AD² + ( � AB)² [∵ AB = BC]

⇒ AB² = AD² + ( �AB)²

∴ 3AB² = 4AD²