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The area of a room is not enough to determine its dimensions.

First of all, there is no information on its shape: circular, polygonal, a random wobbly shape? There are infinitely many possible shapes.

Even assuming it is rectangular, there are infinitely many possibilities for its dimensions.

Suppose the length of the room is L feet and let W = 570/L be the room's width.

Then for any value of L greater than or equal to 23.9, W < 23.9

and area of the room = L*W = L*(570/L) = 570 sq ft.

Since L can have any one of infinitely many values, the room can have infinitely many possible shapes.

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