Answer: Choice B
[tex]\left\{ \ 3, 5, \sqrt{34} \ \right\}[/tex]
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Explanation:
We'll be using the converse of the pythagorean theorem.
If we had a triangle with sides a,b,c and [tex]a^2+b^2 = c^2[/tex] was true, then we have a right triangle. Note: c is always the longest side
For the first answer choice we have: a = 5, b = 8, c = 12
Then,
[tex]a^2+b^2 = c^2\\\\5^2+8^2 = 12^2\\\\25+64 = 144\\\\89 = 144\\\\[/tex]
which is false. This shows that we do not have a right triangle with sides 5,8,12. This rules out choice A. Choice C is a similar story.
Choice B on the other hand works because
[tex]a^2+b^2 = c^2\\\\3^2+5^2 = (\sqrt{34})^2\\\\9+25 = 34\\\\34 = 34\\\\[/tex]
We have a true statement at the end, which confirms choice B is a right triangle.
