In the figure shown, segment AB is parallel to segment YZ. If AZ = 42 units, BQ = 8 units, and QY = 28 units, what is the length of segment QZ?
If we set line QZ as x, then line AQ would be 42 - x.
QZ = x
AQ = 42 - x
BQ = 8
QY = 28
The first thing to note is that triangle ABQ is similar to triangle ZYQ.
That also means that the side length ratios are the same.
That means BQ/AQ = QY/QZ
BQ/AQ = QY/QZ can be written as 8/(42 - x) = x/28.
8/(42 - x) = x/28
1176 - 28x = 8x
1176 = 36x
x = 98/3
Since x is QZ, our answer is 98/3.
However, I am not the most confident.
I hope this helped. :)))))