ABC is an equilateral triangle of side 2a. Find each of its altitudes.
Let AD be the altitude in the given equilateral triangle, ΔABC.
We know that altitude bisects the opposite side.
∴ BD = DC = a
∠ADB = 90º
Applying pythagoras theorem we obtain
AD2 + DB2 = AD2
⇒ AD2 + a2 = (2a)2
⇒ AD2 + a2 = 4a2
⇒ AD2 = 3a2
⇒ AD =`asqrt3`
In an equilateral triangle, all the altitudes are equal in length. Therefore, the length of each altitude will be `sqrt3a`
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