Abstract: A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this talk I will show that there exist infinitely many rational parametrizations, in terms of $s$, of rational triangles with perimeter $2s(s+1)$ and area $s(s^2-1)$. As a corollary, there exist arbitrarily many Heron triangles with all the same area and the same perimeter. The proof uses an elliptic K3 surface $Y$. If time permits, I will also sketch how to find the N\'eron-Severi group of $Y$ and the Mordell-Weil group of the generic fiber.