Because ΔYXW is similar to ΔSTR, we know that each of their corresponding line segments are related to each other by the same proportion. This is because when two triangles are similar, one is a scaled-down version of the other.
Based on how the triangles are defined, we can see that point Y corresponds to point S, point X corresponds to point T, and point W corresponds to point R. This helps us see which line segments correspond to each other (e.g., WY corresponds to RS, and XY corresponds to TS).
We have our corresponding line segments, and we know that each pair of corresponding line segments will create the same proportion. In other words, (WY/RS) is equal to (XY/TS), both of which are also equal to (WX/RT). Written as an equation:
WY / RS = XY / TS
The problem gives us 3 of those values and asks us to find the 4th, XY. Plugging in our known values:
24 / 16 = XY / 8
Cross-multiplying gives us:
16XY = 24(8)
Solving for XY:
16XY = 192
16XY / 16 = 192 / 16
XY = 12
