The diagonal of a square is 8 cm. Determine the length of each side (in cm). Use the standard relation between the diagonal and side of a square.

Introduction / Context: This geometry question uses the Pythagorean relation in a square: diagonal = side * √2. Given the diagonal, we invert the relation to find the side length.

Given Data / Assumptions:

• Diagonal d = 8 cm.
• Relation for a square: d = s * √2, where s is the side.
• Use √2 ≈ 1.414 for numerical value.

Concept / Approach: Rearrange the identity to s = d / √2. Then substitute the known values for a quick computation.

Step-by-Step Solution: s = d / √2 = 8 / √2. √2 ≈ 1.414 ⇒ s ≈ 8 / 1.414 ≈ 5.656. Rounded to two decimals: s ≈ 5.66 cm. The closest listed option is 5.64 cm.

Verification / Alternative check: Check: s * √2 ≈ 5.656 * 1.414 ≈ 8.00, matching the given diagonal.

Why Other Options Are Wrong: 2 cm, 2.8 cm, and 1.414 cm are far from the required side of approximately 5.66 cm.

Common Pitfalls: Confusing side with diagonal or using √2 ≈ 1.4, which can give slightly off results. Use a more precise √2 for accuracy.

Final Answer: 5.64 cm