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agentx5
Group Title
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
 2 years ago
agentx5 Group Title
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
 2 years ago

This Question is Closed

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
Make sense? ^_^
 2 years ago

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
24 hrs later and nobody has attempted this? :/
 2 years ago

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

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

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

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

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
358? Why one less?
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
This 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. :)
 2 years ago

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
what about h?
 2 years ago

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

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

mukushla Group TitleBest ResponseYou've already chosen the best response.2
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
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
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 ...
 2 years ago

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