Absolutely impossible you would be mad to even consider it!!!!!!!!!!! choose Petra ..most people were really disappointed with The dead sea.
No not possible and like the other poster says Petra is the one to choose....do the Dead Sea on your next trip!!!!!!
NO way you can do both.
Petra is a ful day as the walk down is about 2 miles long but worth it for the views and scenery.
It takes a long time and yes u have to come back up so sensible shoes as its very sandy at times, Wear something with a good sole.
Take your camera.
Well Well wsorth it.