let

l = the length of the rectangle

w = the width of the rectangle, w>0

A = 66 yd^2 the area of the rectangle

the length of a rectangle is 1 yd more than double the width:

l = 1 + 2w

the area of the rectangle is 66 yd^2:

l*w = 66

plug l = 1 + 2w into the last equation:

(1 + 2w)*w = 66

by solving we find:

w = 5.5 yd

click here to see the step by step solution of the equation:

l = 1 + 2*5.5 = 12 yd

the dimensions of the rectangle are: the width is 5.5 yd and the length is 12 yd.