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The area is not sufficient information to determine the dimensions.
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 you assume that it is a rectangle, there are infinitely many possible answers.
Let L > sqrt(299) = 17.29 ft be a length and let B = 299/L ft. Then a rectangular room of L ft *B ft will have an area of L*B = L*(299/L) = 299 sq ft. Since the choice of L is arbitrary, there are infinitely many possible answers.
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