Interesting problem

To better describe the problem I have uploaded here:

Feel free to ask any questions.

Any help is appreciated!

Here is the picture:

FMH114179.jpg

It seems pretty straightforward to me. You have the proportions of the ellipse from A, and the scale factor P, so you can write an equation for the ellipse. Now you also know the proportions of B, so you can write an equation of a diagonal of B using its aspect ratio as slope. Find where this line intersects the ellipse, and you have found the corners of the scaled B.

Have you done that? Where are you having trouble?
 
Yeah I suppose its straightforward. I have not attempted it as of yet. I will proceed as you described and update results.
 
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