Draw a "proportional" buffer

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I'm working on aquatic vegetation and have a shapefile representing floating vegetation in a lake. By some studies, we know that submerged vegetation extends for a certain extension based on floating vegetation (e.g. submerged vegetation extends 3 times floating vegetation).I'd like to draw potential submerged vegetation extension, so I'd need something like a "proportional buffer" drawing a polygon slight where the original polygon is slighter and larger where the original polygon is larger, and the resulting buffer distance has to be the result of the width of the original polygon multiplied by a given value (e.g. 3).I know this is difficult, but does exist a way of doing it?

I attach an image where the brown polygons represent the floating vegetation and the red polygon, drawn by eye, should represent the result I'm looking for (more or less)

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