Answer:
2√(13)
Explanation:
The Pythagorean theorem says that the longest side of a right triangle is equal to:
[tex]c=\sqrt[]{a^2+b^2}[/tex]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:
[tex]\begin{gathered} c=\sqrt[]{6^2+4^2} \\ c=\sqrt[]{36+16} \\ c=\sqrt[]{52} \end{gathered}[/tex]Finally, simplifying the radical, we get:
[tex]\begin{gathered} c=\sqrt[]{52} \\ c=\sqrt[]{4(13)} \\ c=\sqrt[]{4}\text{ }\sqrt[]{13} \\ c=2\text{ }\sqrt[]{13} \end{gathered}[/tex]Therefore, the length of the missing side is 2√(13)
