# Aspect Ratio with two rectangles

This is probably simpler that I'm making it (it would have to be), but I'm stuck and don't even quite know how to language this.

Imagine I have two boxes; one has a width of 3/4 of the whole, and the other is the remaining 4th. They are side by side and initially have 0 height.

I fill box-1 (3/4) box with an object that is 100% wide and who's height is determined based on aspect ratio. So box-1 stretches to the height of this object and keeps it same width. Box-2 still has the same width (1/4th of the whole) and zero height. Using aspect ratio I want to create an object that will fill box-2 and match the height of box-1, but I can't figure out how to calculate said aspect ratio.

Specifically - the aspect ratio of the item in box-1 is currently 4.5:1 and using trial and error I got the heights to match with ~1.6:1 in box-2; but I have no idea if that is reliable or if it will work consistently.

Any help?

A Drawing:

• It would help a great deal if you drew a picture and labeled the various lengths with letters like $a,b,c,\ldots$. The question as written is very difficult to understand. Feb 21, 2015 at 0:55
• I understand completely. Hopefully the drawing helps.
– dgo
Feb 21, 2015 at 1:21
• According to your drawing, you need to set $y=1$. Also, $4.5$ is three-quarters of 6, so you need to set $x=1.5$. Feb 21, 2015 at 1:22
• Although your answer was, in retrospect, hilariously obvious, it unfortunately isn't working in practice. I think the reasons why may involve other variables that fall outside of the purview of this math problem. The logic of your answer is what I was looking for though; so thank you.
– dgo
Feb 21, 2015 at 17:55
• My pleasure. This was still a useful exercise, as it uncovered that the real issue is not the math but the "other variables". Feb 21, 2015 at 17:57