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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 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.
Let L feet be any length greater than sqrt(352) = 18.8 ft.
And let W = 352/L. Then any LxW rectangle will have an area of L*W = L*352/L = 352 square feet. There are infinitely many choices for L and so there are infinitely many possible answers.
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