The given figure can be redrawn as:
In the above figure, triangle BAD is similar to triangle CBD.
Therefore, the ratio of corresponding sides of the triangles CBD and ABD will be equal.
[tex]\frac{CB}{AB}=\frac{BD}{AD}=\frac{CD}{BD}[/tex]
Hence,
[tex]\begin{gathered} \frac{BD}{AD}=\frac{CD}{BD} \\ BD^2=AD\times CD \\ n^2=5\times15 \\ n^2=75 \end{gathered}[/tex]
Now applying Pythagoras theoerm to right triangle BAD,
[tex]\begin{gathered} AB^2=BD^2+AD^2 \\ m^2=n^2+5^2 \\ m^2=75+25 \end{gathered}[/tex]
Solve the equation to find m.
[tex]\begin{gathered} m^2=100 \\ m=\sqrt[]{100} \\ m=10 \end{gathered}[/tex]
Therefore, the value of m is 10.
