Five congruent rectangles. What’s their proportion width : height (aspect ratio)?

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## Solution

The aspect ratio is 2+√3.

As can be seen from the diagonal, one can fit a brick in the middle sharing two vertices with the slanted brick. Now from the four vertical line segments shown, it is easily seen that point C lies halfway a standing brick. This makes triangle ABC a 30-60-90 triangle. Therefore α=15° and the aspect ratio is 1/tan(15°)=2+√3.