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FoolForMath
 3 years ago
Another super easy problem,
If an ant wants to crawl over the rectangular block of dimensions \( 6\times5\times4 \) from one vertex to a diagonally opposite vertex, what is the shortest distance it would need to travel?
FoolForMath
 3 years ago
Another super easy problem, If an ant wants to crawl over the rectangular block of dimensions \( 6\times5\times4 \) from one vertex to a diagonally opposite vertex, what is the shortest distance it would need to travel?

This Question is Closed

rebeccaskell94
 3 years ago
Best ResponseYou've already chosen the best response.1Is it a flying ant?

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.1Read the question carefully Parth.

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.1Bingo ninhi5! \(\sqrt{117} \) is the right answer.

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.0The ant needs to travel one side, and one diagonal. We have three cases: side '4' + diagonal of (6 and 5) = 4 + sqrt61= 11.something side '6' + diagonal of (4 and 5) = 6 + sqrt41= 12.something side '5' + diagonal of (4 and 6) = 5 + sqrt52 =12.something hence shortest = 4 + sqrt61

SmoothMath
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1338100316725:dw\[\sqrt{x^2 + 5^2} + \sqrt{(6x)^2 + 4^2}\] By the pythagorean theorem, the sum of those two diagonals is: To minimize this distance, derive and set equal to 0.

ninhi5
 3 years ago
Best ResponseYou've already chosen the best response.1dont make it over complicated :)

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.0Oh damn! I completely forgot that !! :/ Damn my soul

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.1There are only 3 possible roots, consistent to Smooth's diagram.

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.1@ninhi5: Can you post the explanation?

SmoothMath
 3 years ago
Best ResponseYou've already chosen the best response.1I let Alpha do the derivation and optimization for me. http://www.wolframalpha.com/input/?i=solve+%28x%2F%28sqrt%28x%5E2%2B25%29%29++%286x%29%2F%28sqrt%28%286x%29%5E2%2B16%29%29%29+%3D0%2Cx

ninhi5
 3 years ago
Best ResponseYou've already chosen the best response.1i just use pythogorean theorem

SmoothMath
 3 years ago
Best ResponseYou've already chosen the best response.1So x = 10/3, giving this distance: http://www.wolframalpha.com/input/?i=sqrt%28%2810%2F3%29%5E2%2B5%5E2%29%2Bsqrt%28%286%2810%2F3%29%29%5E2%2B4%5E2%29

rebeccaskell94
 3 years ago
Best ResponseYou've already chosen the best response.1can antonia travel around the outside of the box?
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