As we can see in the given diagram, the segment PT measures 14.4 inches and is also being cut into 4 approximately equal parts.
Let's equal the length of each smaller segment by dividing 14.4 inches by 4.
Therefore, each smaller segment measures 3.6 inches.
As we can see in the diagram, the segment QT is equal to 3 smaller segments (QR, RS, and ST).
To get the measure of segment QT, let's multiply 3.6 inches by 3.
Therefore, the measure of segment QT is 10.8 inches.