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

$\begin{gathered} 3=6p \\ p=\frac{3}{6}=\frac{1}{2} \end{gathered}$

We use this value to find HJ

$HJ=5p=5\cdot\frac{1}{2}=\frac{5}{2}$

Therefore, HJ is 5/2 units long.