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Suppose the area is a rectangle of length L ft and breadth B ft, so that L > B > 0.

Then Perimeter = 36 ft => L + B = 18 so that L = 18 - B

Then Area = 45 sq ft = L*B = (18 - B)*B

B2 - 18B + 45 = 0 => (B - 3)*(B - 15) = 0

So B = 3 => L = 15

or B = 15 => L = 3

Then L>B => Length = 15 ft, Breadth = 3 ft

All this assumes the area is a rectangle. It could, however, be an ellipse, or some other shape.

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Q: What is the dimension of a 45 sq ft area with 36 ft perimeter?
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