Question

Points Q, R, and S are collinear, and R is between Q and S as shown at the right. If QS = 15 units and RS = 1/3QR, what is the length of RS?

Answer 1

From the above figure, QS = QR + RS. Let QR = x unit. So,

`\begin{gathered} QS=QR+RS \\ \Rightarrow15=x+(1)/(3)x \\ \Rightarrow15=(4)/(3)x \\ \Rightarrow45=4x \\ \Rightarrow(45)/(4)=x \end{gathered}`

So, we get QR = 45/4 units.

Now, RS = 1/3 QR. So,

`\begin{gathered} RS=(1)/(3)QR \\ \Rightarrow RS=(1)/(3)*(45)/(4) \\ \Rightarrow RS=(15)/(4) \end{gathered}`

Thus, RS = 15/4 units.