The height of an equilateral triangle is `sqrt(3)` a units . Then , its side is _________ units .

Answer

To find the side length of an equilateral triangle given its height, we can follow these steps:

### Step 1: Understand the relationship between the height and the side of an equilateral triangle.
For an equilateral triangle, the height (h) can be expressed in terms of the side length (a) using the formula:
\[ h = \frac{\sqrt{3}}{2} a \]

### Step 2: Substitute the given height into the formula.
We are given that the height of the triangle is \(\sqrt{3} a\). Therefore, we can set up the equation:
\[ \sqrt{3} a = \frac{\sqrt{3}}{2} a \]

### Step 3: Solve for the side length (a).
To eliminate \(\sqrt{3}\) from both sides, we can divide both sides by \(\sqrt{3}\):
\[ a = \frac{1}{2} a \]
Now, we can multiply both sides by 2 to isolate \(a\):
\[ 2h = a \]
Substituting \(h = \sqrt{3} a\):
\[ 2(\sqrt{3} a) = a \]
This simplifies to:
\[ a = 2\sqrt{3} a \]

### Step 4: Rearranging the equation.
Now, we can rearrange the equation to find \(a\):
\[ a = 2\sqrt{3} \]

### Final Answer:
Thus, the side length of the equilateral triangle is \(2\) units.

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