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Ferningur hefur hliðarlengdina x = 56 cm.

Reiknaðu þvermál hrings sem hefur sama ummál og ferningurinn.

Námundaðu svarið að tíundahluta, einingin er cm

The problem involves finding the diameter of a circle that has the same perimeter (circumference) as a square with a side length of \( x = 56 \) cm.

### Step 1: Calculate the perimeter of the square.
The perimeter \( P \) of a square is given by:
\[
P = 4 \times \text{side length}
\]
For \( x = 56 \) cm:
\[
P = 4 \times 56 = 224 \, \text{cm}
\]

### Step 2: Relate the perimeter of the square to the circumference of the circle.
The circumference \( C \) of a circle is given by:
\[
C = \pi \times d
\]
where \( d \) is the diameter of the circle.

Since the circle has the same perimeter as the square, set \( C = P \):
\[
\pi \times d = 224
\]

### Step 3: Solve for the diameter \( d \).
\[
d = \frac{224}{\pi}
\]
Now, let's compute the value of \( d \).The diameter of the circle that has the same perimeter as the square is approximately \( 71.3 \) cm.

Would you like any further explanation or have any additional questions?

Here are five related questions to consider:
1. How would the diameter change if the side length of the square was doubled?
2. What is the area of the circle with the calculated diameter?
3. How does the area of the square compare to the area of the circle with the same perimeter?
4. How do you find the radius of a circle given the diameter?
5. If the side length of the square were reduced to half, what would be the new diameter of the circle?

**Tip:** The perimeter of a square grows linearly with its side length, while the circumference of a circle grows with the diameter at a rate proportional to \( \pi \).

Ferningur hefur hliðarlengdina x = 56 cm. Reiknaðu þvermál hrings sem hefur sama ummál og ferningurinn. Námundaðu svarið að tíundahluta, einingin er cm.

Calculate the diameter of a circle that has the same perimeter as a square with side length 56 cm. Learn how to use key geometric concepts, including perimeter and circumference, and apply the relation between them. Suitable for Grades 8-10.

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