Still more on oriented containers and containees...

This post continues this earlier post here and this overflow question.

https://arxiv.org/abs/2001.09525 proves results on the minimum area isosceles triangle that contains a given general triangle. I understand results on the minimum perimeter isosceles triangle containers of triangles also have been derived. Here we record some further questions.

1. Which planar convex region maximizes the difference between the isosceles triangles of least area and least perimeter that contain it - this difference can be quantified by the ratio between areas of the least area and least perimeter isosceles containers?

2. Which planar convex region maximizes the difference between right triangles of least area and least perimeter that contain it?

Note: Analogous questions can be asked with other types of containers (for example, kites, as was done here).