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# Answer to Question #7374 in Geometry for gaurav

Question #7374
An ant lives on the surface of a cube with edges of length 7cm. It is currently located on an edge x cm which is 2cm 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 which is also equal to 2 cm from one of its ends) (i) What is the length of the shortest route to the grain if x = 2cm? How many routes of this length are there?javascript:void(0) (ii) Find an x for which there are four distinct shortest length routes to the grain. what r the steps followed?
(I) The shortest way is 2+7+7+2 = 18 sm. There are 2 such ways.
(II) For x=3.5 sm (middle of the edge) there are 4 such ways.

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Assignment Expert
11.11.15, 16:59

Dear Harmi.
Thank you for correcting us.

Harmi
05.11.15, 11:33

(i) Ant first move to the corner then move through the diagonal to the corner nearest to the grain then move to the grain.
Total distance covered = 2+length of diagonal+2
=4+sqrt(7*7+7*7)
=4+9.8995
=13.8995