If is an equilateral triangle such that, then AD² =

Given in an equilateral ΔABC, AD ⊥ BC

Since AD ⊥ BC, BD = CD = BC/2

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 ADC,

⇒ AC² = AD² + DC²

⇒ BC² = AD² + DC²

⇒ (2DC)² = AD² + DC²

⇒ 4DC² = AD² + DC²

⇒ 3DC² = AD²

∴ 3CD² = AD²