[tex]m=\sqrt[]{125}[/tex]
1) Examining that right triangle, and deriving from the similarity ratios, we can write down the following formulas:
[tex]\begin{gathered} n^2=20\cdot5 \\ n^2=100 \\ \sqrt[]{n^2}=\sqrt[]{100} \\ n=10 \end{gathered}[/tex]
Note that in this equation, we are not taking into consideration the negative 10 as a possible result since dimensions can only be written as positive numbers.
2) Now, with the length of the height (n) we can find the length of that hypotenuse m using this formula:
[tex]\begin{gathered} m^2=25\cdot5 \\ \sqrt[]{m^2}=\sqrt[]{25\cdot5} \\ m=\sqrt[]{125} \end{gathered}[/tex]
And that is the answer.
