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agentx5

  • 3 years ago

Mental Puzzle! ^_^ First, please view this question: http://openstudy.com/study#/updates/500c014fe4b0549a892fe7dc Now my question is this: How many combinations of WHOLE # units are there for the dimensions that can yield that total area? To be clear: No fractions. No roots. No irrationals. No imaginary #'s. Just strictly whole # units, how many combinations are possible? Have at it math people! I look forward to seeing your methods! (please don't just post your combination total, show us what you did to do it)

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  1. agentx5
    • 3 years ago
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    For reference: an isosceles trapezoid with an area of 21540 ft\(^2\) http://mathworld.wolfram.com/IsoscelesTrapezoid.html

  2. agentx5
    • 3 years ago
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    Make sense? ^_^

  3. agentx5
    • 3 years ago
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    Related example done, to show visually what I mean |dw:1342968040706:dw| 1m * 16m = 16m\(^2\) is also valid, however... 2\(\sqrt{2}\)m * 4\(\sqrt{2}\)m = 16 m\(^2\) gives the right area, sure; but is INVALID for this question, whole units only. \(\sqrt{2}\) isn't a whole number :-)

  4. agentx5
    • 3 years ago
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    24 hrs later and nobody has attempted this? :-/

  5. mukushla
    • 3 years ago
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    hi agentx5 u mean to find all integers (a,b,h) such that \( (a+b) h=2*21540= 2^3 * 3 * 5 * 359 \)

  6. agentx5
    • 3 years ago
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    Err I believe so yes... All positive integers that yield a final area from that formula that is 21540 units\(^2\) :-)

  7. agentx5
    • 3 years ago
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    I'm just going to close it in a few if nobody is interested in trying the puzzle, it was more for fun & learning than "an answer for a homework problem" or anything like that. Saw the previous question (see link) and though it would be an interestingly related question. ;-)

  8. mukushla
    • 3 years ago
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    it seems we have a nice combination problem workin on it...

  9. mukushla
    • 3 years ago
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    oh oh but this is really a Mental Puzzle ; so many answers ; just with letting a+b=359 u have 358 answers...o.O

  10. agentx5
    • 3 years ago
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    358? Why one less?

  11. agentx5
    • 3 years ago
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    This type of geometrical combination puzzle is the kind the like what security systems use on the new-style touch-screen lockpads for vaults and such. The human user has to remember only a 3D shape, but an algorithm to solve it would be much harder. :-)

  12. mukushla
    • 3 years ago
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    nice... and 358 because a,b>0 a=1,2,...,358 consedering symmetry for a and b u have 358 answers

  13. agentx5
    • 3 years ago
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    what about h?

  14. agentx5
    • 3 years ago
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    The height of the trapezoid?

  15. mukushla
    • 3 years ago
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    if u let a+b=359 then there is one valur for height; and that is 3*5*8

  16. mukushla
    • 3 years ago
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    value***

  17. mukushla
    • 3 years ago
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    number of divisors of area=8*3*5*359 is (3+1)(1+1)(1+1)(1+1)=32 h can be all of them like h=1 or 2 or 359

  18. mukushla
    • 3 years ago
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    after chossing 'h' u must find answers for a+b=(area/h) so there are many many answers its better to do it with computer i think ...

  19. agentx5
    • 3 years ago
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    Alright well I'm impressed at you for giving it the ol' college try :-D ty!

  20. mukushla
    • 3 years ago
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    yw :)

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