Pythagorean triples are used to determine if a triangle is a right triangle or not.
The legs of 16 units and an odd number cannot be a right triangle
The Pythagorean triples are given by:
[tex]x^2 - y^2\\[/tex], [tex]2xy[/tex] and [tex]x^2 + y^2[/tex]
- Given that one of the side lengths is 16 units.
- The other side length can be represented as k + 1, where k is a non-negative even integer.
So, we have:
[tex]x^2 + y^2 = 16^2 + (k + 1)^2[/tex]
Take square roots of both sides
[tex]\sqrt{x^2 + y^2} = \sqrt{16^2 + (k + 1)^2}[/tex]
[tex]\sqrt{x^2 +y^2} = \sqrt{256 + k^2 + 2k + 1}[/tex]
Collect like terms
[tex]\sqrt{x^2 + y^2} = \sqrt{256 + 1+ k^2 + 2k }[/tex]
[tex]\sqrt{x^2 +y^2} = \sqrt{257+ k^2 + 2k }[/tex]
Rewrite the above equation as:
[tex]\sqrt{x^2 +y^2} = \sqrt{k^2 + 2k + 257}[/tex]
In the above equation, [tex]k^2 + 2k + 257[/tex] cannot be expressed as a perfect square.
Hence, the lengths of 16 and an odd number cannot be a right triangle
Read more about Pythagorean triples at:
https://brainly.com/question/16314667
