Question

If the length of a side in a square is 'x', then the diagonal will be:

• A. \( \sqrt{2} \times x \)
• B. \( 2x \)
• C. \( \sqrt{3} \times x \)
• D. \( 3x \)

Hint:

The diagonal of a square is \( \sqrt{2} \times \text{side length} \).

Answer 1

The Correct Option is A

Step 1: Understanding the Diagonal of a Square. 
The diagonal of a square forms a right triangle with two sides of the square. Using the Pythagorean theorem, the length of the diagonal \( d \) is given by: \[ d = \sqrt{x^2 + x^2} = \sqrt{2x^2} = \sqrt{2} \times x. \] Step 2: Verifying the Options. 

- Option (1): The correct formula for the diagonal is \( \sqrt{2} \times x \). 
- Option (2): \( 2x \) is incorrect for the diagonal. 
- Option (3): \( \sqrt{3} \times x \) is incorrect. 
- Option (4): \( 3x \) is incorrect. 
Conclusion: 
Therefore, the correct answer is (1) \( \sqrt{2} \times x \).