Question

ABC is an equirateral triangle of side 2​A find each of its altitudes​

Answer 1

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Answer 2

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Let ABC be an equilateral triangle with each of its sides 2A.

Also, AD is one of the altitudes of △ABC.

In △ADB, <ADB = 90°

•°• By Pythagorus Theorem

AB² = AD² + BD²

=> (2a)² = AD² + a² [°•° BD = 1/2 BC]

=> AD² = 4a² - a²

=> AD = √3a²

=> AD = √3a

Hence, its altitude measures √3a.