The mis-stacked trays

A rectangle is turned 90°, bisecting a bigger rectangle of the same shape. When squares are removed from the two side pieces, the remaining rectangles have the same shape as well. What is the common ratio of the rectangle side lengths?

Scroll down for a solution to this problem.


The ratio b/a is approximately 1,84.

Solution by Stéphane Bernard.

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One reply on “The mis-stacked trays”

Rather disappointed that the question required a non-exact solution to a cubic but, hey ho, one does not get a “nice” answer every time.
Equating the 3 side ratios leads to k^3 – k^2 – k – 1=0 where k=b/a. This has a solution k = 1.8395 approx.
You can also use gradients (para & perp) to arrive at the same cubic.

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