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Each edge of the above cube has length 1. If an ant

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Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 17 Jun 2018, 07:29
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C
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Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions

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Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 17 Jun 2018, 09:01
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GMATPrepNow wrote:
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Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions


There can be two shortest distance..
1) A fly in the centre of box moving from ptA to pt B..
It will be the diagonal of cube
2) an ant that has to move on surface...
It will be a line joining A and B along the surface..

Here we are looking at case 2
So when we join A and B, ut creates a triangle ( imagine that you open two sides that A and B are on same plane..
So the triangle becomes a right angle triangle with base along A as 2 sides of cube so 2 *1=2
The altitude along B is one side so 1
Hypotenuse AB = \(√(2^2+1^1)=√5\)

C
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Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 17 Jun 2018, 09:35
Is it the path on the right cube?
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 18 Jun 2018, 01:23
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GMATPrepNow wrote:
Image
Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions


Since, ant has to go through the surface thus we just have to imagine that cube is not on a 3d but a 2d plane, ie we open the cube. Now AB will the hypotenuse that we have to find and the base will be 1+1=2 and Perpendicular =1 so H^2=2^2+1^2=4+1=5
H^2=5 so H=\sqrt{5} answer C
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 18 Jun 2018, 03:23
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1

Solution



Given:
    • Each edge of the above cube has length 1
    • An ant walks from point A to point B along the outside of the cube

To find:
    • The shortest distance the ant must travel

Approach and Working:
Although the cube is a 3-D figure, if we unfold the surfaces containing points A and B respectively, we get a figure like this:

Image

As the ant is at point A and needs to go at point B, with shortest possible distance,
    • The minimum distance the ant needs to cover = \(\sqrt{[(1+1)^2 + 1^2]} = \sqrt{5}\)

Hence, the correct answer is option C.

Answer: C
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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New post 20 Jun 2018, 05:35
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GMATPrepNow wrote:
Image
Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions


If we open up the cube, we get something like this....
Image

Let x = the distance from A to B
Image
Since we have a right triangle, we can apply the Pythagorean Theorem to get: 1² + 2² = x²
Simplify to get: 1 + 4 = x²
So, 5 = x², which means x = √5

Answer: C

Cheers,
Brent
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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Re: Each edge of the above cube has length 1. If an ant   [#permalink] 24 Jul 2019, 01:04
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