The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths
and corresponds to the Pythagorean triple 
where the legs have lengths 3
and 4 and the hypotenuse length 5. It satisfies the
Pythagorean theorem since
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(1)
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It has inradius
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(2)
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Triangle line picking for points picked at random in a 3, 4, 5 triangle gives a mean line segment length of
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(3)
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(4)
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(E. W. Weisstein, Aug. 6-9, 2010; OEIS A180307).
