Hello, fabxx!

In the figure below, points $\displaystyle P, A, B$ are equally spaced,

and points $\displaystyle P, Q, R$ are equally spaced.

If $\displaystyle PB=4,\;PR=6,\;AQ=4$, what is the perimeter of quadrilateral $\displaystyle QABR$ ?

Rotate the diagram 90°. Code:

P
o
* *
3 * * 2
* *
Q o * * * * * o A
* 4 *
3 * * 2
* *
R o * * * * * * * * * * * o B
?

We have: $\displaystyle \Delta PBR$

$\displaystyle QA$ joins the midpoints of two sides.

Hence, $\displaystyle QA \parallel RB$ and $\displaystyle QA = \frac{1}{2}(RB)$

Therefore: .$\displaystyle RB \:=\:8$