Answer
The width of the field is $50$ yards, and the length is 100 yards.
Work Step by Step
Let the width of the field be $ w.$
We are told that the length is $2w.$
The perimeter equals 2$\times $(width + length)
=$2(w+2w)=2(3w)=6w $
Given $6w=300$
We divide with $6$.
$ w=50$
Thus, the width of the field is $50$ yards, and the length is 100 yards.