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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?
 one year ago
 one year 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?
 one year ago
 one year ago

This Question is Closed

rebeccaskell94Best ResponseYou've already chosen the best response.1
Is it a flying ant?
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.1
No No, http://www.nooooooooooooooo.com/
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.1
Read the question carefully Parth.
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.1
Bingo ninhi5! \(\sqrt{117} \) is the right answer.
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
The 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
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.1
dw: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.
 one year ago

ninhi5Best ResponseYou've already chosen the best response.1
dont make it over complicated :)
 one year ago

apoorvkBest ResponseYou've already chosen the best response.0
Oh damn! I completely forgot that !! :/ Damn my soul
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.1
There are only 3 possible roots, consistent to Smooth's diagram.
 one year ago

binary3iBest ResponseYou've already chosen the best response.1
dw:1338145571548:dw
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.1
@ninhi5: Can you post the explanation?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.1
I 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
 one year ago

ninhi5Best ResponseYou've already chosen the best response.1
i just use pythogorean theorem
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.1
So 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
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.1
can antonia travel around the outside of the box?
 one year ago
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