1. **State the problem:** We have an equilateral triangle with side length 7 units. 2. **Understand the transformation:** The triangle is translated 3 units to the right. 3. **Recall the property of translation:** Translation moves every point of a shape the same distance in the same direction without changing its size or shape. 4. **Apply the property:** Since translation does not affect side lengths, the side length remains the same. 5. **Final answer:** The length of one side of the triangle after the translation is still $7$ units.