Answer:
2√(13)
Step-by-step explanation:
The Pythagorean theorem says that the longest side of a right triangle is equal to:
![c=\sqrt[]{a^2+b^2}](https://img.qammunity.org/2023/formulas/mathematics/college/6uwqakmkjq6nua21bpopztkrf20jt2flji.png)
Where a and b are the length of the other sides.
So, replacing a by 6 and b by 4, we get that the largest side of the triangle is equal to:
![\begin{gathered} c=\sqrt[]{6^2+4^2} \\ c=\sqrt[]{36+16} \\ c=\sqrt[]{52} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/u4h9hesn1pi5dzgetju4soa9np5v72tb3l.png)
Finally, simplifying the radical, we get:
![\begin{gathered} c=\sqrt[]{52} \\ c=\sqrt[]{4(13)} \\ c=\sqrt[]{4}\text{ }\sqrt[]{13} \\ c=2\text{ }\sqrt[]{13} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/6b12tqgf2vctym5zpin032i0nk82i0xl8j.png)
Therefore, the length of the missing side is 2√(13)