Take into account that you have two right triangles inside the bigger triangle. Then, by using the Pythagorean theorem in the smaller triangle, you have:

for one of the legs of the bigger triangle you obtain:

where c is a leg of the bigger triangle. For the second interior triangle:

Now, replace the expression for c^2 of the second equation, in the third equation and solve for n^2:

Then, solve for n^2 in the first equation, replace the obtained result into the pervious equation and solve for m, as follow:
![\begin{gathered} n^2=m^2-5^2^{} \\ m^2-5^2=(20+5)^2-20^2-m^2 \\ m^2+m^2=(20+5)^2-20^2+5^2 \\ 2m^2=25^2-20^2+5^2 \\ 2m^2=625-400+25 \\ m^2=(250)/(2) \\ m=\sqrt[]{125}=\sqrt[]{5\cdot25}=5\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ysn3naafs0rjcbvix1gd2a9uudzibem9vh.png)
Hence, the value of m is m = 5√5