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 = 90^{O}

Using Pythagoras theorem, we get

AD^{2} + DB^{2} = AB^{2}

AD^{2} + a^{2} = (2a)^{2}

AD^{2} + a^{2} = 4a^{2}

AD^{2} = 3a^{2}

AD = a

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

Hence, the length of each altitude will be

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation