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:
![KJ^2=KM^2+MJ^2](/tpl/images/0661/1154/7f058.png)
![KJ^2=6^2+3^2](/tpl/images/0661/1154/ee760.png)
![KJ^2=36+9](/tpl/images/0661/1154/2baa1.png)
![KJ^2=45](/tpl/images/0661/1154/99c08.png)
Now we will take positive square root on both sides:
![\sqrt{KJ^2}=\sqrt{45}](/tpl/images/0661/1154/aafb7.png)
![KJ=\sqrt{9\cdot 5}](/tpl/images/0661/1154/1c222.png)
![KJ=3\sqrt{5}](/tpl/images/0661/1154/88c74.png)
Therefore, the length of line segment KJ is
and option D is the correct choice.
![What is the length of line segment KJ? 2 \sqrt{3} units 3 \sqrt{2} units 3 \sqrt{3} units 3 \sqrt{5}](/tpl/images/0661/1154/9c3a8.jpg)