Find the measurement of QT, if ST = 6

[alee]

Points P, W, R, S, and T are all collinear. RP = PS, PQ = QR, and PS = ST. T is not between R and S. If ST = 6, find the measurement of QT.

Thank you very much.

 

[Denis]

Points P, W, R, S, and T are all collinear. RP = PS, PQ = QR, and PS = ST. T is not between R and S. If ST = 6, find the measurement of QT.

I presume W is Q :shock:

T.....2x.....S.....2x.....P..x..Q..x..R

OK?

 

[soroban]

Hello, alee!

Take baby-steps and make lots of diagrams . . .

Points $\displaystyle P,\,W,\,R,\,S,\,T$ are collinear.

$\displaystyle RP\,=\,PS,\;PQ \,=\,QR,\;PS\,=\,ST.\;\;T$ is not between $\displaystyle R$ and $\displaystyle S$.

If $\displaystyle ST\,=\,6$, find the length of $\displaystyle QT$.

$\displaystyle RP\,=\,PS.\;$ Let $\displaystyle RP\,=\,2x$

      :    2x     :    2x     :
      *-----------*-----------*
      R           P           S

$\displaystyle PQ\,=\,QR$

      :  x  :  x  :    2x     :
      *-----*-----*-----------*
      R     Q     P           S

$\displaystyle PS\,=\,ST.\;\;T\text{ is not between }R\text{ and }S.$

      :  x  :  x  :    2x     :    2x     :
      *-----*-----*-----------*-----------*
      R     Q     P           S           T

We are told that: $\displaystyle \,ST\,=\,6\;\;\Rightarrow\;\;2x\,=\,6\;\;\Rightarrow\;\;x\,=\,3$

Now we can find the length of any line segment in the diagram . . .