The question asks which square has the greatest perimeter, given that one of the dimensions of each square is marked as 7 meters.

Let’s examine each option:

1. Option A: The side of the square is labeled directly as 7 meters. Since the perimeter $P$ of a square is calculated as $P = 4 \times \text{side}$, the perimeter here would be: $P = 4 \times 7 = 28 \text{ meters}$

2. Option B: Here, 7 meters is marked across a diagonal of the square. For a square with a diagonal $d$, the side $s$ can be found using the formula $s = \frac{d}{\sqrt{2}}$. Therefore: $s = \frac{7}{\sqrt{2}} \approx 4.95 \text{ meters}$ Then, the perimeter would be: $P = 4 \times 4.95 \approx 19.8 \text{ meters}$

3. Option C: The side of the square is labeled as 7 meters, similar to Option A. Therefore, the perimeter here would also be: $P = 4 \times 7 = 28 \text{ meters}$

4. Option D: In this square, 7 meters is labeled as part of the diagonal. Using the same calculation as in Option B, the side length would be approximately 4.95 meters, giving a perimeter of: $P = 4 \times 4.95 \approx 19.8 \text{ meters}$

Conclusion: Options A and C each have a perimeter of 28 meters, which is the largest perimeter among the options.

So, the answer is either Option A or Option C.

Would you like further details or have any other questions?

Related Questions:

1. How would you calculate the area of each square in the options?
2. What if the diagonal was labeled as 7 meters for a non-square rectangle? How would the perimeter calculation change?
3. How can we find the side length of any square if only the diagonal is known?
4. Why does labeling the diagonal lead to a smaller perimeter than labeling the side?
5. Could a different shape with a diagonal of 7 meters have a larger perimeter than the squares?

Tip:

To solve problems involving squares, remember that the diagonal relates to the side by a factor of $\sqrt{2}$. This can be useful for quickly finding the side when only the diagonal is given.