Question

In an equilateral triangle ABC, if AD is perpendicular to BC, then
(a) 2 AB^2 = 3 AD^2 (b) 4 AB^2 = 3 AD^2 (c) 3 AB^2= 4 AD^2
(d) 3 AB^2= 2 AD^2​

Answer 1

Answer:

c)3 AB² = 4 AD²

Step-by-step explanation:

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