If w is the width and l the length the length of the rectangular field, then, based on the given information, you can write:
2w + 2l = 240 perimeter
l=2w
Replace the expression for l into the equation for the perimeter and solve for w:
2w + 2(2w) = 240
2w + 4w = 240
6w = 240
w = 240/6
w = 40
then, for the length l you obtain:
l = 2(40) = 80
Then, the dimensions of the field are 80 yards x 40 yards
width = 40 yd
length = 80 yd