[tex]\begin{gathered} \text{From Pythagoras theorem,} \\ (6\sqrt[]{5})^2=(4\sqrt[]{5})^2+m^2 \\ 36(5)=16(5)+m^2 \\ 180=80+m^2 \\ m^2=180-80 \\ m^2=100 \\ m=\sqrt[]{100} \\ m=10\text{ cm} \end{gathered}[/tex][tex]\begin{gathered} \text{The perimeter of the triangle is the sum of the three sides} \\ =10\operatorname{cm}\text{ + 6}\sqrt[]{5}\text{ cm + 4}\sqrt[]{5}\text{ cm} \\ =\text{ (10 + 10}\sqrt[]{5})cm \\ or\text{ } \\ \text{10(1+}\sqrt[]{5})\text{ cm} \end{gathered}[/tex]
