[tex]DF=10[/tex]
1) Since this is a right triangle, and no information about angles has been given. It is safe to say that we can use the Pythagorean Relation to figure out the length of that hypotenuse DF
2) So we can write it down:
[tex]\begin{gathered} a^2=b^2+c^2 \\ DF^2=DE^2+EF^2 \\ DF^2=6^2+8^2 \\ DF^2=36+64 \\ DF^2=100 \\ \sqrt[]{DF^2}=\sqrt[]{100} \\ DF=-10,10 \end{gathered}[/tex]
Since there are no negative lengths, we can state that the answer is:
[tex]DF=10[/tex]
