ABC is an equilateral triangle of side 2a. Find each of its altitudes.
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 + a2
⇒ AD2 = 4a2 - a2
⇒ AD2 = 3a2
⇒ AD = √3a
