Let’s analyze the problem:

Translation and Analysis:

Alexis has a square table with sides of 2 meters. The store only has a round tablecloth with a diameter of 2.5 meters. The question is: Is this tablecloth large enough to fully cover the table? Justify your response.

Step-by-Step Solution:

1. Area and Coverage Check:

   • The diagonal of the square table is the longest dimension that needs to be covered by the tablecloth. For a square table with side length $s$, the diagonal $d$ is given by: $d = s\sqrt{2}$ Substituting $s = 2$: $d = 2\sqrt{2} \approx 2.83 \, \text{meters.}$

2. Tablecloth Size:

   • The round tablecloth has a diameter of 2.5 meters, which means its radius is: $r = \frac{2.5}{2} = 1.25 \, \text{meters.}$
     • The total coverage diameter of the tablecloth is 2.5 meters.

3. Comparison:

   • To fully cover the table, the diagonal of the square table ($2.83 \, \text{meters}$) must be less than or equal to the diameter of the tablecloth ($2.5 \, \text{meters}$).
   • However, $2.83 > 2.5$, so the tablecloth is not large enough to fully cover the table, particularly along its diagonal.

4. Conclusion: The round tablecloth will not fully cover Alexis's square table. Alexis would need a larger tablecloth with a diameter at least equal to the diagonal of the table ($2.83 \, \text{meters}$).

Would you like me to clarify anything further or expand on this?

Follow-Up Questions:

1. What is the formula for the area of a circle, and could the tablecloth cover in terms of area?
2. How does the shape of the table (square) affect the tablecloth’s coverage compared to a circular table?
3. What would the required diameter of a tablecloth be to fully cover this table?
4. How is the diagonal of a square calculated, and why is it important here?
5. Could a rectangular table have a different diagonal length compared to a square table of the same area?

Tip:

Always calculate the diagonal of a square table when determining if a round tablecloth will fit—it represents the maximum dimension needing coverage!