Which of the following equations expresses a relationship between D. (September 2023 - G01)

Correct answer: B. D = √2S.

To find the relationship between the length of the diagonal (D) and the length of a side (S) of a square, we can use the Pythagorean theorem. In a square, the diagonal divides the square into two congruent right triangles.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the lengths of the other two sides (the sides of the square).

So, we have:
D² = S² + S²
D² = 2S²

To solve for D, we take the square root of both sides:
D = √2S²
D = √2 * S
So, the correct answer is B