please assist me with these problems using the 45-45-90 relationship triangles

Answer:
see below
Step-by-step explanation:
side opposite 90 angle = x [tex]\sqrt{2}[/tex]
sides opposite 45 angle = x
the multiplication and division by [tex]\sqrt{2}[/tex] should be self explanatory
1. x = 5, y = 5
2. v = 10, u = 10
3. x = [tex]\sqrt{10}[/tex], y = [tex]\sqrt{5}[/tex]
4. m = 5, n = [tex]\frac{5\sqrt{2} }{2}[/tex]
5. a = [tex]\frac{3\sqrt{2} }{2}[/tex], b = [tex]\frac{3\sqrt{2} }{2}[/tex]
6. a = [tex]\frac{3\sqrt{2} }{2}[/tex], b = [tex]\frac{3\sqrt{2} }{2}[/tex]