If the perimeter of a square is 44 cm, what is the diagonal (in cm) of the square ?

Options

A. `11sqrt(2)`
B. `2sqrt(11)`
C. 11
D. `44sqrt(2)`

Answer

To find the diagonal of a square when the perimeter is given, we can follow these steps:

### Step 1: Understand the formula for the perimeter of a square.
The perimeter \( P \) of a square is given by the formula:
\[ P = 4 \times \text{side} \]

### Step 2: Set up the equation using the given perimeter.
We know from the problem that the perimeter is 44 cm. Therefore, we can write:
\[ 4 \times \text{side} = 44 \]

### Step 3: Solve for the side length.
To find the length of one side of the square, we divide both sides of the equation by 4:
\[ \text{side} = \frac{44}{4} = 11 \text{ cm} \]

### Step 4: Use the formula for the diagonal of a square.
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = \text{side} \times \sqrt{2} \]

### Step 5: Substitute the side length into the diagonal formula.
Now that we have the side length, we can substitute it into the formula for the diagonal:
\[ d = 11 \times \sqrt{2} \]

### Step 6: Write the final answer.
Thus, the diagonal of the square is:
\[ d = 11\sqrt{2} \text{ cm} \]