Consider this option:
if new map is bigger 3 times then old one, it means that the new area is bigger 3 times then the old one. And if the area is 3 times bigger, the side is bigger √3 times.
Using the rules described above it is possible to calculate new scale of the map:
12*√3≈12*1.7=20.78461 yards in 1 inch.
If it is possible check the suggested solution in other sources.