Although the rug shown has a classic Turkish design, it appears as
though the pattern does not translate to the reverse of the rug. It
may be a power-loomed piece, perhaps a Wilton rug which were popular
alternatives to hand knotted rugs at the time.
This cover was illustrated by Joseph Leyendecker who was the main illustrator of the Saturday Evening Post before Norman Rockwell. He ended up illustrating 322 covers for the Post between 1899 and 1943, with his later years not having as many commissions.
What a picture perfect painting. Although the best option for
cleaning a rug is to bring it to your local professional, rug beaters
do pop-up on ebay from time to time.
Saturday Evening Post May 11,1940.