**Equilateral Triangle:**

An equilateral triangle is a type of triangle in which all three sides are equal in length. In an equilateral triangle, all three angles are also equal to 60 degrees.

**Given Information:**

In the given question, triangle ABC is an equilateral triangle of side 2a.

**Altitude of an Equilateral Triangle:**

The altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side or the line containing the opposite side.

In an equilateral triangle, the altitude is also the median and the angle bisector. It can be divided into two equal segments by the centroid of the triangle.

**Finding the Altitude:**

To find the altitude of an equilateral triangle, we can use the Pythagorean theorem.

Let's consider triangle ABC. The given side length is 2a. We need to find the altitude, which we'll denote as h.

**Using the Pythagorean theorem:**

In a right triangle formed by the altitude, half of the base, and the altitude itself, we can apply the Pythagorean theorem:

(hypotenuse)^2 = (base/2)^2 + (altitude)^2

In this case, the hypotenuse is the side of the triangle, which is 2a, the base is half of that, which is a, and the altitude is h.

(2a)^2 = a^2 + h^2

4a^2 = a^2 + h^2

3a^2 = h^2

h = sqrt(3a^2)

Therefore, the altitude (h) of an equilateral triangle with side 2a is sqrt(3a^2).

**Conclusion:**

In conclusion, the altitude of an equilateral triangle with side 2a is equal to sqrt(3a^2). This can be obtained by applying the Pythagorean theorem and solving for the altitude using the given side length.