What are the missing side lengths for the triangle?

Answer:
[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]
Step-by-step explanation:
In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:
[tex]BC=5\sqrt{2}[/tex]
To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.
[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]