1. **State the problem:** We have an equilateral triangle with side length 14 cm. When folded in half, it forms a right triangle where $x$ is the height (altitude) of the equilateral triangle. 2. **Recall properties:** In an equilateral triangle, all sides are equal and all angles are 60°. 3. **Folding the triangle:** Folding the equilateral triangle in half creates a right triangle with angles 30°, 60°, and 90°. 4. **Use 30-60-90 triangle rules:** In a 30-60-90 triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where the hypotenuse is twice the shortest leg. 5. **Identify sides:** The hypotenuse is the original side of the equilateral triangle, 14 cm. 6. **Calculate the height $x$:** The height corresponds to the longer leg opposite the 60° angle, so $$x = \frac{\sqrt{3}}{2} \times 14$$ 7. **Simplify:** $$x = 7\sqrt{3}$$ 8. **Approximate value:** $$x \approx 7 \times 1.732 = 12.124$$ cm **Final answer:** $$x = 7\sqrt{3} \approx 12.12 \text{ cm}$$