A Tale of Two Right Angled Triangles

You are given two right-angled triangles. You are given their side lengths. The first triangle is ABC, where side AB is the hypotenuse. Length of AB is **c**, that of AC is **b**, and that of BC is **a**. Similarly, the second triangle is DEF, where DE is the hypotenuse. Length of DE is **f**, that of DF is **e**, and that of EF is **d**. First, we define *minimum area enclosing axis-parallel rec