Using the Pythagorean Theorem, it is found that the lengths could be given by:
A. 6, 8, 10.
What is the Pythagorean Theorem?
The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Hence, in item a:
[tex]h^2 = 6^2 + 8^2[/tex]
[tex]h^2 = 100[/tex]
[tex]h = 10[/tex]
So it is a right triangle.
Item b:
[tex]h^2 = 2^2 + 5^2[/tex]
[tex]h^2 = 29[/tex]
[tex]h = \sqrt{29} \neq 100[/tex]
It is not a right triangle.
Item c:
[tex]h^2 = 5^2 + 6^2[/tex]
[tex]h^2 = 61[/tex]
[tex]h = \sqrt{61} \neq 7[/tex]
It is not a right triangle.
Item d:
[tex]h^2 = 2^2 + 3^2[/tex]
[tex]h^2 = 13[/tex]
[tex]h = \sqrt{13} \neq 5[/tex]
It is not a right triangle.
Hence option a is correct.
More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982
