Please consider the attached file.
We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.
We will use Pythagoras theorem to solve for KJ as:
[tex]KJ^2=KM^2+MJ^2[/tex]
[tex]KJ^2=6^2+3^2[/tex]
[tex]KJ^2=36+9[/tex]
[tex]KJ^2=45[/tex]
Now we will take positive square root on both sides:
[tex]\sqrt{KJ^2}=\sqrt{45}[/tex]
[tex]KJ=\sqrt{9\cdot 5}[/tex]
[tex]KJ=3\sqrt{5}[/tex]
Therefore, the length of line segment KJ is [tex]3\sqrt{5}[/tex] and option D is the correct choice.
