how to check date is older than x days in shell script

datetime='2016-08-31T15:38:18Z'
timeago='90 days ago'

dtSec=$(date --date "$datetime" +'%s')
taSec=$(date --date "$timeago" +'%s')

echo "INFO: dtSec=$dtSec, taSec=$taSec" >&2

[ $dtSec -lt $taSec ] && echo too old