How can I correctly adjust the height of a plot made with ggplot2 when saving to PDF using ggsave?

Question

I created two plots with different aspect ratios, adjusted them with theme(aspect.ratio = ...) and joined them into a single picture using the patchwork package.

When I save the picture as a PDF, I need the width to be 10 cm, but the height of the picture isn't defined because it depends on the aspect ratio I've indicated for each plot and the caption.

I used ggsave to save the picture as a PDF, specified a width of 10 cm and didn't set the height, thinking that it would be adjusted automatically. The height was adjusted automatically but left a lot of blank space.

When I don't specify the aspect ratio of each plot, the PDF picture takes up all the available area. How can I get the same result by specifying the aspect ratio of each plot?

library(ggplot2)
library(patchwork)

p1 <- ggplot(data = mtcars,
             aes(x = cyl,
                 y = hp,
                 color = as.factor(vs))) +
  geom_line() +
  theme(aspect.ratio = 0.5)

p2 <- ggplot(data = mtcars,
             aes(x = mpg,
                 y = carb,
                 color = as.factor(vs))) +
  geom_line() +
  theme(aspect.ratio = 0.25)

p <- p1 / p2 +
  plot_annotation(tag_levels = "a",
                  tag_prefix = "(",
                  tag_suffix = ")") +
  plot_layout(guides = 'collect') &
  theme(legend.position='bottom')

ggsave("example.pdf",
       plot = p,
       width = 10,
       #height = ??,
       units = "cm",
       device = cairo_pdf)

Example with a specified aspect ratio

Example without a specified aspect ratio