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 2 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)
 2 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)

This Question is Closed

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1For reference: an isosceles trapezoid with an area of 21540 ft\(^2\) http://mathworld.wolfram.com/IsoscelesTrapezoid.html

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Related 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 :)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.124 hrs later and nobody has attempted this? :/

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2hi agentx5 u mean to find all integers (a,b,h) such that \( (a+b) h=2*21540= 2^3 * 3 * 5 * 359 \)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Err I believe so yes... All positive integers that yield a final area from that formula that is 21540 units\(^2\) :)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1I'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. ;)

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2it seems we have a nice combination problem workin on it...

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2oh oh but this is really a Mental Puzzle ; so many answers ; just with letting a+b=359 u have 358 answers...o.O

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1This type of geometrical combination puzzle is the kind the like what security systems use on the newstyle touchscreen 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. :)

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2nice... and 358 because a,b>0 a=1,2,...,358 consedering symmetry for a and b u have 358 answers

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1The height of the trapezoid?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2if u let a+b=359 then there is one valur for height; and that is 3*5*8

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2number 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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.2after 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 ...

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Alright well I'm impressed at you for giving it the ol' college try :D ty!
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