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ABC is an equilateral triangle of side 2a. Find each of its altitudes.

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ABC is an equilateral triangle of side 2a. 

Draw, AD ⊥ BC

In ΔADB and ΔADC, we have

AB = AC [Given]

AD = AD [Given]

∠ADB = ∠ADC [equal to 90°]

Therefore, ΔADB ≅ ΔADC by RHS congruence.

Hence, BD = DC [by CPCT]

In right angled ΔADB, 

AB2 = AD2 + BD2

(2a)2 = AD2 + a

⇒ AD2  = 4a2 - a2

⇒ AD2  = 3a2 

⇒ AD  = √3a 

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