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Review: Distance within a Box
Explanation
It's usually a good idea to make a quick sketch on
geometry questions:
The lengths of all of the edges of this shape are either 5
or 10. The lines joining points 
,
,
and so on, are all 10. The length 
is the hypotenuse of a triangle with sides 5
and 10, so its length is
by the Pythagorean Theorem. However, 
is
not the longest segment connecting two points. Namely, 
is longer because it is the hypotenuse of a
triangle that has 
as a base, so its length is 
These are the two-longest lines connecting two points on the
box, so the sought-after ratio is 
The correct answer is (A).
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