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

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#### Solution

Let AD be the altitude in the given equilateral triangle, ΔABC.

We know that altitude bisects the opposite side.

∴ BD = DC = *a*

In ΔADB

∠ADB = 90º

Applying pythagoras theorem we obtain

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

⇒ AD^{2} + a^{2} = (2a)^{2}

⇒ AD^{2} + a^{2} = 4a^{2}

⇒ AD^{2} = 3a^{2}

⇒ AD =`asqrt3`

In an equilateral triangle, all the altitudes are equal in length. Therefore, the length of each altitude will be `sqrt3a`

Concept: Right-angled Triangles and Pythagoras Property

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