Question

J is between H and K. If HJ=5p, JK=p, and KH=3, find HJ.

Answer 1

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

`KH=HJ+JK`

Replacing given equations and values, we have

`3=5p+p`

Then, we solve for p

`\begin{gathered} 3=6p \\ p=(3)/(6)=(1)/(2) \end{gathered}`

We use this value to find HJ

`HJ=5p=5\cdot(1)/(2)=(5)/(2)`

Therefore, HJ is 5/2 units long.