The area of a square is twice the area of a circle. The area of the circle is `392 cm^2`. What is the length of the side of the square?

Options

A. 28 cm
B. 26 cm
C. 24 cm
D. 22 cm

Explanation

To find the length of the side of the square given that the area of the square is twice the area of a circle, we can follow these steps:

### Step 1: Identify the area of the circle
The area of the circle is given as \( 392 \, \text{cm}^2 \).

### Step 2: Calculate the area of the square
Since the area of the square is twice the area of the circle, we can calculate the area of the square as follows:
\[ \text{Area of the square} = 2 \times \text{Area of the circle} \]
\[ \text{Area of the square} = 2 \times 392 \, \text{cm}^2 = 784 \, \text{cm}^2 \]

### Step 3: Use the area to find the side length of the square
The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
Let \( s \) be the length of the side of the square. Therefore:
\[ s^2 = 784 \, \text{cm}^2 \]

### Step 4: Solve for the side length
To find \( s \), we take the square root of both sides:
\[ s = \sqrt{784} \, \text{cm} \]
Calculating the square root:
\[ s = 28 \, \text{cm} \]

### Conclusion
The length of the side of the square is \( 28 \, \text{cm} \).

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