A square table has a side of 1 meter. What is the smallest diameter (in meters) of a round tablecloth that can completely cover the tabletop?
(a) 1
(b) 1.5
(c) 2
(d) $\sqrt{2}$
(e) $\sqrt{3}$
The correct option is (d).

For the tablecloth to completely cover the table and have the smallest possible diameter, the square must be inscribed in the circle. The diagonal of the square is the diameter of the circle, so by the Pythagorean Theorem, we have $d^{2}=1^{2}+1^{2}$, that is, $d=\sqrt{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-057.jpg?height=232&width=237&top_left_y=1226&top_left_x=1640)