If the perimeter of a square is 80 cm, then what is the diagonal of the square (in cm) ?

Options

A. `20sqrt(2)`
B. `40sqrt(2)`
C. `80sqrt(2)`
D. 20

Answer

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

### Step-by-Step Solution:

1. **Understand the Perimeter of a Square**:
The perimeter (P) of a square is calculated using the formula:
\[ P = 4 \times \text{side} \]
where "side" is the length of one side of the square.

2. **Set Up the Equation**:
Given that the perimeter of the square is 80 cm, we can set up the equation:
\[ 4 \times \text{side} = 80 \]

3. **Solve for the Side Length**:
To find the length of one side, divide both sides of the equation by 4:
\[ \text{side} = \frac{80}{4} = 20 \text{ cm} \]

4. **Calculate the Diagonal**:
The diagonal (d) of a square can be calculated using the formula:
\[ d = \text{side} \times \sqrt{2} \]
Substituting the value of the side we found:
\[ d = 20 \times \sqrt{2} \text{ cm} \]

5. **Final Answer**:
Therefore, the length of the diagonal of the square is:
\[ d = 20\sqrt{2} \text{ cm} \]