Answer:
7.1 cm
Explanation:
Let s represent the side length of the square. The Pythagorean theorem tells you the relationship to the diagonal length is ...
(10 cm)² = s² +s² . . . . the sum of the squares of the legs is the square of the hypotenuse
100 cm² = 2s² . . . . . . simplify
50 cm² = s² . . . . . . . . divide by 2
√(50) cm = s ≈ 7.1 cm . . . . . take the square root
The length of a side of the square to the nearest tenth is 7.1 cm.