Question

in the figure below, s is between q and t, and r is the mid - point of $overline{qs}$. if $rs = 6$ and $rt = 8$, find $qt$.

Explanation:

Step1: Find length of QS

Since R is the mid - point of $\overline{QS}$ and $RS = 6$, then $QS=2\times RS$.
$QS = 2\times6=12$

Step2: Find length of QT

We know that $QT=QS + ST$. Also, $ST=RT - RS$. Given $RS = 6$ and $RT = 8$, then $ST=8 - 6 = 2$. And since $QS = 12$, then $QT=QS+ST$.
$QT=12 + 2=14$

Answer:

$14$