The diagram shows a square with one side marked as s, while the diagonal that cuts across measures 6 units.
The diagonal results in a right angled triangle with two sides measuring 45 degrees and one side measuring 90 degrees. Now that we have a right angled with one angle, and two sides (one is given as 6, and one is unknown), we now calculate side s as follows;
[tex]\begin{gathered} \cos 45=\frac{\text{adj}}{\text{hyp}} \\ We\text{ use the ratio for cosine because the sides shown are the} \\ \text{adjacent (between the right angle and the reference angle) and} \\ \text{hypotenuse (facing the right angle)} \\ \cos 45=\frac{s}{6} \\ \cos 45=\frac{1}{\sqrt[]{2}} \\ \text{Therefore,} \\ \frac{1}{\sqrt[]{2}}=\frac{s}{6} \\ \text{Cross multiply and you have} \\ \frac{6}{\sqrt[]{2}}=s \\ \text{Rationalize the expression and you have} \\ 3\sqrt[]{2}=s \\ \text{Therefore} \\ s=3\sqrt[]{2} \end{gathered}[/tex]The correct answer is option E