Solution
For A.
Using Pythagoras theorem
[tex]\begin{gathered} AB^2+AC^2=BC^2 \\ \\ \Rightarrow AC^2=BC^2-AB^2 \\ \\ \Rightarrow AC=\sqrt[]{BC^2-AB^2} \\ \\ \Rightarrow AC=\sqrt[]{10^2-9^2}=\sqrt[]{100-81}=\sqrt[]{19} \end{gathered}[/tex]
For B
Using Pythagoras theorem
[tex]\begin{gathered} EF^2+FD^2=DE^2 \\ \\ \Rightarrow EF^2=DE^2-FD^2 \\ \\ \Rightarrow EF^{}=\sqrt[]{DE^2-FD^2} \\ \\ \Rightarrow EF^{}=\sqrt[]{7^2-4^2}=\sqrt[]{49-16}=\sqrt[]{33} \end{gathered}[/tex]
For C
Using Pythagoras theorem
[tex]\begin{gathered} JH^2+GH^2=JG^2 \\ \\ \Rightarrow JG=\sqrt[]{JH^2+GH^2} \\ \\ \Rightarrow JG=\sqrt[]{6^2+5^2}=\sqrt[]{61} \end{gathered}[/tex]
