To solve the problem, here’s the process:

1. Determine the side length of the square:

   • The perimeter $P$ of a square is given by $P = 4 \times \text{side length}$.
   • Here, $P = 20$ cm. So, the side length is: $\text{side length} = \frac{P}{4} = \frac{20}{4} = 5 \, \text{cm}.$

2. Find the diagonal of the square:

   • The diagonal of a square can be calculated using the Pythagorean theorem: $\text{diagonal} = \sqrt{\text{side}^2 + \text{side}^2} = \sqrt{2 \times \text{side}^2}.$
   • Substituting the side length $5 \, \text{cm}$: $\text{diagonal} = \sqrt{2 \times 5^2} = \sqrt{2 \times 25} = \sqrt{50}.$
   • Simplify: $\text{diagonal} = 5\sqrt{2} \, \text{cm} \approx 7.07 \, \text{cm}.$

Final Answer:

The length of the diagonal is approximately $7.07 \, \text{cm}$.

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:

1. How does the Pythagorean theorem apply to other shapes beyond squares?
2. What is the relationship between the diagonal and the side length of a square?
3. Can you derive a formula for the diagonal in terms of the perimeter directly?
4. How does the diagonal change if the perimeter doubles?
5. What are some real-world applications of calculating diagonals in geometry?

Tip: When solving geometry problems, always identify relationships between the given information (like perimeter) and the unknowns (like side lengths or diagonals). This approach simplifies problem-solving!