ANSWER
A. 8cm
EXPLANATION
The diagonal of the square is
[tex]d = 8 \sqrt{2} cm[/tex]
Let the length of each side of the square be l units.
Then the diagonal and any two sides form an isosceles right triangle with the diagonal being the hypotenuse.
We use the Pythagoras Theorem, to obtain,
[tex] {l}^{2} + {l}^{2} = {d}^{2} [/tex]
This implies that,
[tex]2 {l}^{2} = (8 \sqrt{2} )^{2} [/tex]
[tex]2{l}^{2} = 128[/tex]
Solve for l,
[tex]{l}^{2} = 64[/tex]
Take positive square root of both sides
[tex]l = \sqrt{64} [/tex]
[tex]l = 8cm[/tex]
