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Since the ratio QR:RS:ST is 1:1:3, we can express the lengths of the segments as follows:
QR = x
RS = x
ST = 3x
Given that QT = 10, we have:
QT = QR + RS + ST
10 = x + x + 3x
10 = 5x
x = 2
Therefore, QR = RS = 2 and ST = 6.
Now, RT = RS + ST = 2 + 6 = 8.
Therefore, RT = 8.