We know that J is between H and K, this means
As you can observe in the image above, KH is defined by the sum of HJ and JK
[tex]KH=HJ+JK[/tex]
Replacing given equations and values, we have
[tex]3=5p+p[/tex]
Then, we solve for p
[tex]\begin{gathered} 3=6p \\ p=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]
We use this value to find HJ
[tex]HJ=5p=5\cdot\frac{1}{2}=\frac{5}{2}[/tex]
Therefore, HJ is 5/2 units long.
