In an equilateral triangle ABC if , then AD 2 =

Question

Philoid · Accepted Answer

Given in equilateral triangle ABC, 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 ADC,

⇒ AC² = AD² + DC²

⇒ BC² = AD² + DC² [∵ AC = BC]

⇒ (2DC)² = AD² + DC² [∵ BC = 2DC]

⇒ 4DC² = AD² + DC²

⇒ 3DC² = AD²

∴ 3CD² = AD²

In an equilateral triangle ABC if , then AD2 =

In an equilateral triangle ABC if , then AD² =