The distance between opposite corners refers to the diagonal, which we can find using Pythagorean's Theorem where the diagonal is the hypotenuse and the given dimensions are the legs.
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(9m)^2+(12m)^2 \\ c=\sqrt[]{81m^2+144m^2} \\ c=\sqrt[]{225} \\ c=15 \end{gathered}[/tex]