[tex]\begin{gathered} \text{By right triangle altitude theorem} \\ x^2=(8)(5) \\ x^2=40 \\ \sqrt[]{x^2}=\sqrt[]{40} \\ x=2\sqrt[]{10} \end{gathered}[/tex][tex]\begin{gathered} \text{Using the same property as above} \\ y^2=(13)(8) \\ y^2=104 \\ \sqrt[]{y^2}=\sqrt[]{104} \\ y=2\sqrt[]{26} \end{gathered}[/tex]
Summary
[tex]\begin{gathered} \text{Therefore, the missing sides are} \\ x=2\sqrt[]{10} \\ y=2\sqrt[]{26} \end{gathered}[/tex]
