width = 50 and length = 100 For simplicity, we will use the letters W for width, L for length and P

width = 50 and length = 100
For simplicity, we will use the letters W for width, L for length and P for perimeter.
For a rectangular field
##P = 2 * (L + W)##
So we have
##2 * (L + W) = 300##
or ##L + W = 150##
We are told that
##L = W + 50##
So ##L + W = 150## can be re-written as ##(W+50) + W = 150##
which can be simplified:
##2W + 50 = 150##
##2W = 100##
##W = 50##
And since ##L = W +50##
##L = 50 + 50 = 100##
Therefore the width is 50 (yards) and the length is 100 (yards).