Question

AD is an altitude of an equilateral triangle ABC. Prove that : 2AD = √3 AB​

Answer 1

Step-by-step explanation:

In equilateral triangle ABC, AB = BC = CA

Since, AD is perpendicular drawn on side BC,

BD = DC = (1/2) × BC

Now, in ∆ADC, angle ADC = 90°, so

CA^2 = AD^2 + DC^2

4 (DC^2) = AD^2 + DC^2 [Since, CA = BC]

AD^2 = 3DC^2

Hence, proved.