Do the rectangles that circumscribe and share edges with a rhombus have identical dimensions?

Question

I am going to make an app for wrapping presents but I don’t know a lot about useful properties of rhombi and associated rectangles.

Given the known dimensions necessary to create a rhombus that envelopes a cuboid using the diagonal method, what are the resulting dimensions of a rectangle that “circumscribes” it (that’s not the right word, but I don’t know what is), utilizing edges rather than just vertices? Are they identical? (Cutting the rectangles out instead is wasteful, but more practical, given that rolls of paper are used for multiple gifts.)

The pink dimensions are what I’m after.

Update:

I've written code to get the desired result, using vector projection, but I haven't revisited the original question to gain a better understanding yet. Please enlighten!

(.init(dimensions[1], dimensions[2]) + dimensions[0] is a vector representing the pink circumscribed vertex on the right.)

let diagonalOfResult = 2 * (dimensions[2] + dimensions[0])
return
  normalize(
    .init(dimensions[1], dimensions[2]) + dimensions[0]
  )
  * diagonalOfResult