Answer:
625√2 cm
Explanation:
The diagonal of a square is √2 times the side length, so the side length is 1/√2 = (√2)/2 times the length of the diagonal:
s = (√2)/2 × 1250 cm = 625√2 cm
The side length is 625√2 cm.
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Additional comment
A unit square will have sides of length 1. A diagonal of the square will divide it into two right triangles, each with sides of length 1. The Pythagorean theorem tells you the length of the diagonal (d) will be ...
d² = 1² +1² . . . . . . square of hypotenuse is sum of squares of legs
d² = 2 . . . . . . . simplify
d = √2 . . . . . take square root
That is, for any square, the length of the diagonal is √2 times the side length.