Question

charlene has a circular tablecloth with a diameter of 6 feet. she wants to buy a square table that has 4 - foot sides. is the tablecloth big enough to cover the whole surface of the table? why or why not? this cannot be determined, because charlene only measured one side of the table. no, the tablecloth is not big enough, because the diagonal length of the table is 8 feet, which is bigger than the diameter of the tablecloth. yes, the tablecloth is big enough because the side lengths of the table, 4 feet, are smaller than the diameter of the tablecloth, 6 feet.

Explanation:

To cover a square table, the circular tablecloth’s diameter must be at least the square’s diagonal. For a 4-foot square table, the diagonal is calculated using the Pythagorean theorem: $d = s\sqrt{2} = 4\sqrt{2} \approx 5.656$ feet. The tablecloth’s diameter is 6 feet, which is larger than the table’s diagonal (~5.656 feet). Thus, the tablecloth can cover the table.

Answer:

Yes, the tablecloth is big enough because the side lengths of the table, 4 feet, are smaller than the diameter of the tablecloth, 6 feet.