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Answer to BOX OF BEERS:



 

The box sides are  2.414213  units each.

Angle A is a right angle  (being at the junction of the diagonals of the square box).
H is the hypotenuse of the triangle made by lines H, a and b.
Lines a and b are equal .... They each have a length of 1 unit (two half diameters of a can).  
H
^2 = a^2 + b^2. 

So H = square root of 2
H = 1
.414213  units

Lengths c and d are 1/2 can diameter each
Therefore side E = H + c + d
= 1
.414213 + .5 + .5  units
= 2.414213  units

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