Square to diagonal: The area of a square is 100 cm². Find the exact length of its diagonal (in cm).

Introduction / Context:Relating a square’s area to its side and diagonal is routine geometry. If the area is given, the side is the square root of the area, and the diagonal equals side * √2 by the Pythagorean relation in the square’s right triangle.

Given Data / Assumptions:

• Area A = 100 cm².
• Let side = s; diagonal = d.

Concept / Approach:Area of a square: A = s^2 ⇒ s = √A. Diagonal: d = s√2. Keep the exact radical form (no decimals) because the option set is exact with √2.

Step-by-Step Solution:

Verification / Alternative check:If s = 10, the square’s right triangle has legs 10 and 10, so d^2 = 10^2 + 10^2 = 200 ⇒ d = √200 = 10√2, confirming the result.

Why Other Options Are Wrong:10 cm is the side length, not the diagonal; 20 cm and 20√2 cm are too large relative to an area of 100 cm².

Common Pitfalls:Confusing side with diagonal; rationalizing √200 incorrectly.

Final Answer:10√2 cm