[Part 1.] Pack two similar rectangles with aspect ratio r and short sides of length 1 and 2 into a third similar rectangle with short side x, such that the maximum proportion of the larger rectangle is covered.

Find r, x and the proportion covered.

[Part 2.] Pack three similar rectangles with aspect ratio r and short sides of length 1, 2, and 3 into a fourth similar rectangle with short side x, such that the maximum proportion of the larger rectangle is covered.

Find r, x and the proportion covered.