Answers:
length = 8 feet, width = 5.5 feet
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Work Shown:
w = width
2*w = twice the width
2*w-3 = 3 less than twice the width
L = length = 2w-3
area = L*W = (2w-3)*w = 2w^2-3w
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set the area equal to 44, then get everything to one side
2w^2-3w = 44
2w^2-3w-44 = 0
Now use the factor by grouping method
2w^2 - 3w - 44 = 0
2w^2 - 11w + 8w - 44 = 0
(2w^2 - 11w) + (8w - 44) = 0
w(2w - 11) + 4(2w - 11) = 0
(w + 4)(2w - 11) = 0
w+4 = 0 or 2w-11 = 0
w = -4 or w = 11/2 = 5.5
side note: you can use the quadratic formula to solve 2w^2-3w-44 = 0 for w to get the same two solutions as above
A negative width makes no sense, so we'll ignore the first solution. The only practical solution is w = 5.5
Use w = 5.5 to find the length L
L = 2w - 3
L = 2*5.5 - 3
L = 11 - 3
L = 8
So the length is 8 feet and the width is 5.5 feet
As a check: A = L*W = 8*5.5 = 44 which helps confirm the answer.