If the perimeter of a square is 28, what is the length of the diagonal of the square?

Options

A. `2sqrt(14)`
B. `7sqrt(2)`
C. `7sqrt(3)`
D. `14`

Answer

To find the length of the diagonal of a square given its perimeter, 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:
\[ P = 4 \times \text{side length} \]

### Step 2: Set up the equation using the given perimeter.
We know the perimeter of the square is 28. Therefore, we can set up the equation:
\[ 4 \times \text{side length} = 28 \]

### Step 3: Solve for the side length.
To find the side length, we can divide both sides of the equation by 4:
\[ \text{side length} = \frac{28}{4} = 7 \]

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

### 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:
\[ d = 7 \times \sqrt{2} \]

### Step 6: Write the final answer.
Thus, the length of the diagonal of the square is:
\[ d = 7\sqrt{2} \text{ units} \]

### Summary of the solution:
The length of the diagonal of the square is \( 7\sqrt{2} \) units.

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