Q. 6 4.4( 123 Votes )

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

Answer :

Let AD be the altitude of the given equilateral triangle, ΔABC

We know that altitude bisects the opposite side

BD = DC = a

In triangle ADB,

ADB = 90O

Using Pythagoras theorem, we get

AD2 + DB2 = AB2

AD2 + a2 = (2a)2

AD2 + a2 = 4a2

AD2 = 3a2

AD = a

In an equilateral triangle, all the altitudes are equal in length.

Hence, the length of each altitude will be

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