The mirror is a square. The diagonal of the mirror is 10 inches long . The length of the mirror can be calculated below
Therefore, the length is
[tex]\begin{gathered} x^2+x^2=10^2 \\ 2x^2=100 \\ x^2=50 \\ x=\sqrt[]{50} \\ x=\sqrt[]{25\times2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]