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An ant lives on the surface of a cube with edges of length 7cm. It is currently

located on an edge x cm from one of its ends. While traveling on the surface of the cube,
it has to reach the grain located on the opposite edge (also at a distance xcm from one
of its ends) as shown below.
(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of
this length are there?
(ii) Find an x for which there are four distinct shortest length routes to the grain.



I) ant goes northwest to left edge ending 2 =√8=2.83
ii)angles up left side wall to top edge= 2 from top left corner=√50=7.07
iii)then angles directly to grain=√8=2.83
see the attached document
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