Given a Right Triangle, you can use the Pythagorean Theorem to find the length "x", which states that:
[tex]c^2=a^2+b^2[/tex]
Where "c" is the hypotenuse, and "a" and "b" are the legs of the Right Triangle.
In this case, you can set up that:
[tex]\begin{gathered} c=26 \\ a=24 \\ b=x \end{gathered}[/tex]
Then, you can substitute values and solve for "x":
[tex]\begin{gathered} 26^2=24^2+x^2 \\ \sqrt{26^2-24^2}=x \\ x=10 \end{gathered}[/tex]
By definition, you can identify if it is a Pythagorean Triple when "a", "b" and "c" are positive integers and this is true:
[tex]c^2=a^2+b^2[/tex]
In this case, you know that they are positive integers and:
[tex]\begin{gathered} 26^2=24^2+10^2 \\ 676=576+100 \\ 676=676 \end{gathered}[/tex]
Therefore, it is a Pythagorean Triple.
Hence, the answer is:
[tex]x=10[/tex]
It is a Pythagorean Triple.
