To answer this question, we can see that we have a right triangle here. To find the length of the third side, we can apply the Pythagorean Theorem as follows:
[tex]x^2+6^2=(2\sqrt[]{34})^2[/tex]
Then, we have:
[tex]x^2+36=2^2(\sqrt[]{34})^2[/tex]
[tex]x^2+36=4\cdot34\Rightarrow x^2+36=136[/tex]
Therefore, if we subtract 36 from both sides of the equation, we have:
[tex]x^2+36-36=136-36\Rightarrow x^2=100[/tex]
Finally, we have:
[tex]\sqrt[]{x^2}=\pm\sqrt[]{100}\Rightarrow x=\pm10[/tex]
Since the length of a triangle must be positive, then the value for the third side is 10.
In summary, w
