First - You have to check resolution of source data (Landsat pixel size 30mx30m? 50mx50m?). Pixel size speaks much about accuracy, i.e. if your pixel has 30mx30m - You know, that your objects can not be smaller than these dimensions
Second - You need to have reference data, because sometimes even rectified Landsat images have posistion errors; You have to check it out, i.e. just measure distances of all sides of any your polygon to the reference data; You can use OpenStreet data
Georeference of Landsat image using control points from existing maps or GPS surveys gives a good estimation of positional accuracy for each polygon point. From there on you apply the eeror popagation law to estimate any quantity relate to the polygon such as area, perimeter, line segmets, etc.