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  #26  
Old 10-14-2020, 05:51 PM
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Default Re: Geometry puzzle

(60/37)2
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  #27  
Old 10-14-2020, 06:12 PM
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Default Re: Geometry puzzle

Again, Pan wins the prize for the first correct answer!

:medal:

This one was easier (I think) than the last one, but I found it oddly satisfying. The 60 in the answer, one might expect - it is, after all, 3 x 4 x 5 - but I would never have guessed the 37.
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Old 10-15-2020, 08:30 AM
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Default Re: Geometry puzzle

As for how I came to the answer:

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  #29  
Old 10-15-2020, 08:39 AM
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Default Re: Geometry puzzle

Quote:
Originally Posted by ceptimus View Post
Again, Pan wins the prize for the first correct answer!

:medal:

This one was easier (I think) than the last one, but I found it oddly satisfying. The 60 in the answer, one might expect - it is, after all, 3 x 4 x 5 - but I would never have guessed the 37.
Dimensional analysis can work here.

If you figure 3 * 4 * 5 has to be in there, this has units of [length]3. If you want to go to a single [length], you have to divide by [length]2.

One side of the square coincides with the hypothenuse of the triangle, so the 5 warrants special treatment here. To get a [length]2, one might try 3*5 + 4*5 (=35, not quite right) or 3*4 + 5*5 (=37, the right answer).

Of course, this is hand-waving after the fact, but the number 37 does not just pop out of nowhere.
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  #30  
Old 10-15-2020, 01:24 PM
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Default Re: Geometry puzzle

Yes. So my conjecture is that this works for any square drawn in a right triangle.
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Old 10-15-2020, 01:38 PM
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Default Re: Geometry puzzle

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Originally Posted by Pan Narrans View Post
As for how I came to the answer:

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  #32  
Old 10-15-2020, 05:42 PM
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Default Re: Geometry puzzle

As a quick check, here's the 5:12:13 Pythagorean triangle drawn in Fusion 360. You can see that the CAD program puts the dimension for the side of the square in parentheses: in CAD terms this is a "driven dimension" - you can't actually enter a value because the size is already fixed by the dimensions and constraints already specified.



You can see that Fusion 360 shows the length as 3.406, which, to three decimal places, is indeed 780/229
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