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An ant is on the face of a cube with edges measuring five centimeters. The ant starts one centimeter from an edge and two centimeters from another, and wishes to travel to a point on an edge one centimeter from the farthest vertex. What is the shortest distance he can walk along the surface of the cube to accomplish this?

 

This is from a little compilation of problems I found online.. not sure how to solve!!

 Dec 31, 2020
edited by Pangolin14  Dec 31, 2020
edited by Pangolin14  Dec 31, 2020
 #1
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If you use 1+1+1−−−−−−−−√1+1+1, the answer is drilling straight through the cube.

(What a talented ant UwU)

However, we need the ant to go in a path on the surface of a cube, which poses new challenges.

We can quickly visualize the ant going up the cube while going around to the other side.

This, is a straight line along the 1×21×2 rectangle formed by the path.

Therefore, the shortest length is 12+22−−−−−−√=5–√12+22=5.

If you need a more in debt just ask!

-wolfie

 Jan 1, 2021
 #2
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That does not seem to be one of the answer choices. I forgot to include the answer choices with my post, here they are:

 

A) 8 B)10 C) 3√7 D)9 E)√65

 Jan 1, 2021

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