Question

Find the length of the third side. If necessary, write in simplest radical form.2v346

Answer 1

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:

`x^2+6^2=(2\sqrt[]{34})^2`

Then, we have:

`x^2+36=2^2(\sqrt[]{34})^2`

`x^2+36=4\cdot34\Rightarrow x^2+36=136`

Therefore, if we subtract 36 from both sides of the equation, we have:

`x^2+36-36=136-36\Rightarrow x^2=100`

Finally, we have:

`\sqrt[]{x^2}=\pm\sqrt[]{100}\Rightarrow x=\pm10`

Since the length of a triangle must be positive, then the value for the third side is 10.

In summary, w