Question

If one side of an equilateral triangle is \( a \), then its height is:

• A. \( a\sqrt{3} \)
• B. \( \frac{a}{2} \sqrt{3} \)
• C. \( 2a\sqrt{3} \)
• D. \( \frac{a}{\sqrt{3}} \)

Hint:

The height of an equilateral triangle with side length \( a \) is \( \frac{a}{2} \sqrt{3} \).

Answer 1

The Correct Option is B

The height \( h \) of an equilateral triangle with side length \( a \) can be derived using the Pythagorean theorem. The height splits the equilateral triangle into two 30-60-90 right triangles, where the height is given by: \[ h = \frac{a}{2} \sqrt{3}. \] Thus, the correct answer is \( \boxed{\frac{a}{2} \sqrt{3}} \).