Is this set of numbers 1, 2, 3, a Pythagorean Triple?

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Answer 1 · 2016-01-16T16:51:34

No.

The Pythagorean identity states that

#a^2+b^2=c^2#

This is only true in a right triangle where #a,b# are the legs and #c# is the hypotenuse, the longest side.

Thus, if this were a Pythagorean triple, #a=1,b=2,c=3#.

If this indeed is a valid triple, the following statement is true:

#1^2+2^2=3^2#

However, this simplifies to be

#1+4=9#

#5=9#

Which is untrue.

Thus, #1,2,3# is not a Pythagorean triple and sides of such lengths cannot form a right triangle.