Complex math problem, envelope within an area

Hi, I have a complex math problem and I don't know how to start.

I have a rectangular area of certain dimension x mm. Let say, to start with its rotated 45 degrees.

Then I have two lines entering this area with a certain speed. I would like to calculate the combined "envelope" of the two, within this area of investigation. I would like to start placing the centre of the rectangle at the top of the lines.

The lines are the following; line 1 is vertical and line 2 is with a 45 degree angle.

I also want to move the relative position of the lines and the rectangular to each other, i.e. move the lines upward or downward, to find the worst case scenario, i.e. when the combined envelope of the two lines is at the highest I guess.

Any idea suggestions?

Many thanks, /Lizan