Answer:
[tex]x=7,\\y=4\sqrt{2}[/tex]
Step-by-step explanation:
Draw an auxiliary line in the trapezoid forming a triangle and a rectangle. The dimensions of the rectangle are 3 x 4, so the length of the auxiliary line must be 4.
The auxiliary line also creates a 45-45-90 triangle. The auxiliary line itself makes up one leg of the triangle, and since we know it is 4, we can use the Pythagorean Theorem to find y:
[tex]4^2+4^2=y^2,\\y^2=32,\\y=\sqrt{32}=\boxed{4\sqrt{2}}[/tex]
The length of x can be found by adding the bottom leg of the 45-45-90 triangle and the bottom dimension of the rectangle:
[tex]x=4+3=\boxed{7}[/tex]
