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:

For an equilateral triangle with side \( a \), the height is:
\[ h = \frac{a\sqrt{3}}{2}. \]

Answer 1

The Correct Option is B

Using the Pythagorean theorem in an equilateral triangle:
\[ h^2 + \left(\frac{a}{2}\right)^2 = a^2. \] \[ h^2 = a^2 - \frac{a^2}{4}. \] \[ h^2 = \frac{3a^2}{4}. \] \[ h = \frac{a\sqrt{3}}{2}. \]