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April 12th, 2017, 02:22 PM   #1
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Question Conjecture of triangles without infinite decimals

Hi, the conjecture is:

With any combination of angles in a triangle rectangle, is possible to construct a triangle with all its sides without infinite decimals.
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April 12th, 2017, 04:40 PM   #2
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"triangle rectangle" makes no sense in English.

I think what you may be asking is:

Is it possible to construct a right triangle such that the length of each side is an integer multiple of the length of one of the sides?

Yes it is.

Define line segment AB. Extend that line segment by AC and then to AD with equal lengths to that of AB. So line segment AD has length 3. Construct a perpendicular to AD. Find E at 4 times length AB + CD from D. So line segment DE has length 4 times. Join E and A by a straight line. That gives triangle ADE. Line segment AE has length 5 by the Pythagorean Theorem.
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