Question

In an equilateral triangle ABC prove that 3AB² =4AD²​

Answer 1

ΔABD is right-angled at D.

Thus, we can apply Pythagoras' theorem and see that

AB² = AD² + BD²

AB² = AD² + (BC/2)² (since BD = BC/2)

AB² = AD² + (AB/2)² (since AB = BC)

AB² = AD² + AB²/4

3 AB²/4 = AD²

3 AB² = 4 AD²

Therefore, the correct answer is (c).