An Etymological Dictionary of the German Language/Annotated/schlank
schlank, adjective, ‘slender, slim,’ from Middle Low German (Middle German) slanc, ‘slim, lean’; compare Dutch slank, ‘thin, nimble’; to this Old Icelandic slakke (for slanke), ‘mountain slope,’ is also probably allied. Gothic *slanka- would be connected with the root sling in schlingen, like krank with the root kring in Anglo-Saxon cringan; see schlingen.