Discussion

If the side of an equilateral triangle is 'a', what is its altitude?

Answer: C

In an equilateral triangle, the altitude bisects the base. This creates two 30-60-90 right-angled triangles.

The hypotenuse is 'a', the base is 'a/2', and the altitude is 'h'.

Using the Pythagorean theorem: \(h^2 + (a/2)^2 = a^2\)

\(h^2 = a^2 - a^2/4 = \frac{3a^2}{4}\)

\(h = \sqrt{\frac{3a^2}{4}} = \frac{a\sqrt{3}}{2}\).

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