I would say no, as your length and width are not consistently (and somewhat arbitrarily) defined. That is, the areas you wish to measure are relative to the landslide location and orientation and are person-defined.
For example, in the image you post I would say the length is actually the width and the width is actually the length. You define it this way as the landslide originated from the SW to the NW (somewhat), so I get it, but what if the landslide originated from the east and spread to the north of the image?
You could do as the shoreline people do and have all landslide faces (the shorelines) defined as lines and then it would work but you need to define all your origins (landslide lines) as features otherwise only a human knows which is the length and which is the width of the resultant debris field.
This is actually a good problem to address with AI as humans with a priori knowledge can do it easily and explain it easily but preexisting technologies cannot do it automatically as it is almost impossible to solve via a rule-based, pixel-based, or and object-based system even with prior knowledge.