let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A = w*l is the are of the rectangle and A = 44 ft^2

the length of a rectangle is 3ft less than twice the width

l = 2w - 3

the area of the rectangle is 44ft^2

l*w = 44

by replacing l = 2w - 3 in the above equation we have

(2w - 3)w = 44

solving the quadratic equation we find and consider only the positive roots since w>0

w = 5.5 ft

l = 2*5.5 - 3

l = 8 ft

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the dimensions of the rectangle are 8 ft and 5.5 ft.