Final answer:
To find QR, we use the fact that ST bisects PR at T, meaning QT equals ST in length. Solving for n in the equation 2n+48 = 8n+3 gives n = 7.5. Substituting n into QT's expression and doubling it gives QR = 126 units.
Step-by-step explanation:
The question asks us to find the length of line segment QR when segment ST bisects line PR at point T. If ST (which is the same as QT since T is the midpoint) measures 2n+48 and PQ measures 8n+3, then the length of QR will be the same as QT because a bisector divides a line segment into two equal parts. Therefore, the equation to find n is 2n+48 = 8n+3.
Solving for n, we subtract 2n from both sides to get:
48 = 6n + 3.
Then we subtract 3 from both sides to find:
45 = 6n.
We divide both sides by 6 to get:
n = 7.5.
Now that we have the value of n, we can find the length of QR which is twice the length of QT (since ST = QT and QR = 2QT). We substitute n = 7.5 into the expression for QT:
QT = 2n + 48 = 2(7.5) + 48 = 63.
Therefore, QR equals twice the length of QT:
QR = 2 * QT = 2 * 63 = 126.