The problem is asking to calculate the diameter (þvermál) of a circle that has the same circumference as the perimeter of a square with side length $x = 25 \, \text{cm}$.

Step-by-step solution:

1. Find the perimeter of the square: The perimeter of a square is given by: $P_{\text{square}} = 4 \times x$ Substituting $x = 25 \, \text{cm}$: $P_{\text{square}} = 4 \times 25 = 100 \, \text{cm}$

2. Equate the circumference of the circle to the perimeter of the square: The circumference of a circle is given by: $C_{\text{circle}} = \pi \times d$ where $d$ is the diameter. Since the circumference of the circle is the same as the perimeter of the square: $\pi \times d = 100$

3. Solve for the diameter $d$: $d = \frac{100}{\pi}$ Using $\pi \approx 3.1416$: $d = \frac{100}{3.1416} \approx 31.83 \, \text{cm}$

Answer:

The diameter of the circle is approximately $31.8 \, \text{cm}$ when rounded to one decimal place.

Would you like any further details or explanations?

Here are some related questions to deepen your understanding:

1. What is the formula for the area of a circle, and how would it compare to the area of the square?
2. If the square's side length changed, how would the circle's diameter change?
3. How can you express the radius of the circle instead of the diameter?
4. What if the problem asked for a circle with the same area as the square instead of the same perimeter?
5. How would the formula change if this were a 3D shape comparison (e.g., cube and sphere)?

Tip: Always double-check whether the problem asks for circumference, area, or another property to ensure you're solving for the correct variable.