2 by 2 by 3 Right triangle

vadimuha

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Jan 26, 2018
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By playing with toy constructor I stumbled across very interesting construction. If I take a wand as my units of mesure (all wands are the same size) I am able to construct 2:2:3 right triangle which should not be possible. Can you help to figure out what is wrong? (Probably problem is in units of mesure but I would like to see wider explanation)

IMG_20180126_185932.jpgIMG_20180126_185932.jpgIMG_20180126_185932.jpg
 
By playing with toy constructor I stumbled across very interesting construction. If I take a wand as my units of mesure (all wands are the same size) I am able to construct 2:2:3 right triangle which should not be possible. Can you help to figure out what is wrong? (Probably problem is in units of mesure but I would like to see wider explanation)

View attachment 9058View attachment 9058View attachment 9058

Look carefully - each wand is not of same length!!
 
By playing with toy constructor I stumbled across very interesting construction. If I take a wand as my units of mesure (all wands are the same size) I am able to construct 2:2:3 right triangle which should not be possible. Can you help to figure out what is wrong? (Probably problem is in units of mesure but I would like to see wider explanation)

You are ignoring the size of the balls at the vertices!

I straightened out the picture to make it easier to measure (I've been learning photo editing on the side):
FMH109877.jpg
On my screen, at a particular enlargment, each wand is 1.75 inches, and each ball has radius 0.25, approximately. So the legs are 2(1.75) + 2(0.25) = 4 inches, and the hypotenuse is 3(1.75) + 2(0.25) = 5.75.

a^2 + b^2 = 4^2 + 4^2 = 32
c^2 = 5.75^2 = 33

That's close enough, given rounding errors; to put it another way, I'd expect the hypotenuse to be sqrt(32) = 5.66 inches.
 
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