1. **Problem statement:** Find the height $x$ of an equilateral triangle with side length 14 inches. 2. **Formula and rules:** In an equilateral triangle, all sides are equal and all angles are 60°. The height splits the triangle into two 30-60-90 right triangles. 3. **Key property of 30-60-90 triangle:** The sides are in ratio $1 : \sqrt{3} : 2$, where the side opposite 30° is half the hypotenuse, and the side opposite 60° is $\sqrt{3}$ times the shorter leg. 4. **Calculate height:** The base is 14 inches, so half the base is $\frac{14}{2} = 7$ inches (short leg). 5. The height $x$ is the side opposite 60°, so: $$x = 7 \times \sqrt{3}$$ 6. **Final answer:** The height of the equilateral triangle is $7\sqrt{3}$ inches.