Question 6:

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

Answer:

Let AD be the altitude in the given equilateral triangle, ∆ABC.

We know that altitude bisects the opposite side.

∴ BD = DC = a

In ∆ADB,

∠ADB = 90°

Applying  pythagoras theorem, we obtain

AD² + DB² = AB²

⇒ AD² + a² = (2a)²

⇒AD² + a² = 4a²

⇒ AD² = 3a²

⇒AD = a√3

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

Therefore, the length of each altitude will be √3a.

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