Frame png issue with different size display

Frame png issue with different size display

I have a png frame, this frame is 197x458 and is used as background in
some views of an app (that must be similar to the iOS version).
This frame looks fine(with any resolution), but if the display is larger
than 7" (like tablets) the png looks really ugly. I have tried to use
larger version of the frame, but this causes issues with the smaller than
7" dislay .
The issue semms related only with the display size not with the
resolution, so I don't know how should I use the folder hdpi, mdpi and
ldpi
I have see the guidelines
320dp: a typical phone screen (240x320 ldpi, 320x480 mdpi, 480x800 hdpi,
etc).
480dp: a tweener tablet like the Streak (480x800 mdpi).
600dp: a 7" tablet (600x1024 mdpi).
720dp: a 10" tablet (720x1280 mdpi, 800x1280 mdpi, etc)
but I cannot figure how I should scale my 197x458 png to look fine also
with 7" and 10" tablets