Question

If \( \triangle ABC \) is an equilateral triangle of side \( 2a \), the length of each of its altitudes will be:

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

Hint:

The altitude of an equilateral triangle can be found using the formula \( h = \frac{\sqrt{3}}{2} \times \text{side length} \).

Answer 1

The Correct Option is A

Step 1: Understanding the properties of an equilateral triangle.
In an equilateral triangle, all sides are equal, and all angles are \( 60^\circ \). The altitude of an equilateral triangle divides the triangle into two congruent 30-60-90 right triangles.
Step 2: Formula for the altitude in an equilateral triangle.
For an equilateral triangle with side length \( s \), the altitude \( h \) is given by: \[ h = \frac{\sqrt{3}}{2} \times s \]
Step 3: Applying the given side length.
Here, the side length of the triangle is \( 2a \). Therefore, the altitude is: \[ h = \frac{\sqrt{3}}{2} \times 2a = a\sqrt{3} \]
Step 4: Conclusion.
Therefore, the length of each altitude is \( a\sqrt{3} \).