Final answer:
The correct inequality that relates the side lengths of a right triangle, with 'a' being the hypotenuse, is 'a ≥ b ≥ c', since the hypotenuse is the longest side in a right triangle.
Step-by-step explanation:
The question provided is likely related to the properties of triangles and the application of the Pythagorean theorem, which indicates the relation between the sides of a right triangle. Given the references to side lengths and areas of triangles and comparing magnitudes, the inequalities aim to describe these relationships.
Since one reference states that 'a' must be greater than 'c', and another reference points to the Pythagorean theorem where 'c' is the hypotenuse, generally the longest side in a right triangle, we can infer that we are dealing with a triangle where 'a' refers to the hypotenuse. Therefore, the correct option for the side lengths of a right triangle will be 'a' ≥ 'b' ≥ 'c', where 'a' is the hypotenuse and 'b' and 'c' are the other two sides. This is because in a right triangle, the hypotenuse is always the longest side, followed by the other two sides which can be of equal length or one can be longer than the other.