Sofa Moving Problem

or If the Movers Had Been Mathematicians

Some Mathematics

For those of you who wonder what is the mathematics behind this problem, here it is:

Consider the figure on the right. The segment IM is perpendicular to BE. Denote . Then . The triangles AEB and IMB are similar, therefore,

.

From the right triangle ABE we have and by replacing AE and BE we obtain

.

And we have to find the minimum of this function of x.

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