1. **Problem statement:** Given a parabola with focal length $p > 0$, show that the focal width (length of the latus rectum) is $4p$. 2. **Recall the definition:** The focal length $p$ is the distance from the vertex to the focus of the parabola. 3. **Standard form of parabola:** For a parabola with vertex at the origin and focus at $(0,p)$, the equation is $$x^2 = 4py$$ 4. **Latus rectum:** The latus rectum is the line segment through the focus, perpendicular to the axis of symmetry, with endpoints on the parabola. 5. **Find endpoints of latus rectum:** At $y = p$, substitute into the parabola equation: $$x^2 = 4p \cdot p = 4p^2$$ 6. **Solve for $x$:** $$x = \pm 2p$$ 7. **Length of latus rectum:** The distance between the points $(2p, p)$ and $(-2p, p)$ is $$2p - (-2p) = 4p$$ 8. **Conclusion:** The focal width (length of the latus rectum) is $4p$ as required.