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The area is not sufficient information to determine the length and width.

First of all, there is no reason to suppose that the area is rectangular as opposed to circular or triangular or some other simple or complicated shape. Even if, on the basis that the question asks for length and width, you assume that it is a rectangle, there are infinitely many possible answers.

Consider a rectangle whole lenght, L is any number greater than or equal to sqrt(46) units, and let W = 46/L units be its width.

Then area = LxW = Lx46/W = 46 units.

But L is any one of infinitely many numbers, and so there are infinitely many solutions.

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Q: What is the length and width of a shape with an area of 46?
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