Find the length of side X in simplest radical form with a rational denominator.

Answer:
[tex] x = \frac{7 \sqrt{2} }{2} [/tex]
Step-by-step explanation:
[tex] \cos \: 45 \degree = \frac{x}{7} \\ \\ \frac{1}{ \sqrt{2} } = \frac{x}{7} \\ \\ x = \frac{7}{ \sqrt{2} } \\ \\ x = \frac{7 \sqrt{2} }{2} [/tex]