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Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The diagonal splits the square into 2 right triangles, with hypotenuse the diagonal of length 2 and congruent sides x
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
x² + x² = 2²
2x² = 4 ( divide both sides by 2 )
x² = 2 ( take square root of both sides )
x = [tex]\sqrt{2}[/tex] ← length of side of the square