Geometry

Question Analysis
This question tests the understanding of the properties of a 45-45-90 triangle, specifically in the context of a square.

Key Concept Explanation
In a 45-45-90 triangle, the ratio of the lengths of the legs to the hypotenuse is . The diagonal of a square divides it into two 45-45-90 triangles.

Step-by-step Solution
1. Recognize that the diagonal of the square forms the hypotenuse of a 45-45-90 triangle.
2. Use the relationship between the hypotenuse and the legs:
3. Rearrange to solve for the leg(side length):

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