let

l = the length of the rectangle

w = the width of the rectangle

the length of a rectangle is 1ft more than double the width

l = 1 + 2w

the area of the rectangle is 66ft^2

l*w = 66

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

(1 + 2w)w = 66

and find and consider the positive root since the width can not be negative number

w = 5.5 ft

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l = 1 + 2*5.5

l = 12 ft

the dimensions of the rectangle are 5.5 feet and 12 feet.