An Etymological Dictionary of the German Language/schlank

by Friedrich Kluge

schlank, adj., ‘slender, slim,’ from MidLG. (MidG.) slanc, ‘slim, lean’; comp. Du. slank, ‘thin, nimble’; to this OIc. slakke (for slanke), ‘mountain slope,’ is also probably allied. Goth. *slanka- would be connected with the root sling in schlingen, like krank with the root kring in AS. cringan; see schlingen.