Final answer:
Using Pythagoras' theorem, we find that the side length of the square is 4√2 cm when the diagonal is 8√2 cm.
Step-by-step explanation:
To find the length of a side of a square when you know the length of the diagonal, you can use Pythagoras' theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the case of a square, the diagonal forms two congruent right-angled triangles, each with legs that are equal to the length of the sides of the square and the hypotenuse being the diagonal of the square. Since the diagonal is 8√2 cm, we can let x be the length of the side of the square, then apply the theorem: x2 + x2 = (8√2)2. Simplifying this gives us 2x2 = 64, and then x2 = 32, so the length of the side is x = √32 cm. But since √32 is equal to 4√2, the side length of the square is 4√2 cm.