The scale factor is 2.
The scale factor must to be the same for all sides of the triangle. if we have the side A and want to know the scale factor to get A', we can write it like an equation:
[tex]A^{\prime}=r\cdot A[/tex]where r is the scale factor, A is the original side length and A' is the new length.
then, if we look at the hypotenuses:
[tex]\begin{gathered} 10=r\cdot5 \\ r=\frac{10}{5}=2 \end{gathered}[/tex]then the scale factor is 2. to be sure, we can verify this with the other sides
[tex]\begin{gathered} 3\cdot r=3\cdot2=6 \\ 4\cdot r=4\cdot2=8 \end{gathered}[/tex]and all side lengths checks out
