Hi there! Let's solve this problem step by step. :)
We have two triangles, QRP and XYP. You're given a few values.
It is given that QR = 16. QP = 6 + 18. RP = 5 + 15. Go ahead and add those.
QR = 16, QP = 24, RP = 20.
Now XYP!
XY = 12. YP = 15. XP = 18.
If you know the corresponding parts between these triangles--they should be QR to XY, QP to YP, and RP to XP. Those are 16/12, 24/15, and 20/18. Divide those.
You get 1.3333, 1.6, and 1.1111. Your turn! Are they similar?
[P.S., if you're confused about the AA/SAS/SSS similarity postulates, that just means the sides they have in common. You're not given any angle measurements, so SAS (side angle side) is out. SSS is possible, but since the ratios aren't equivalent, SSS is out. Again, AA (angle-angle) isn't possible because you're not given any angle measurements.)
That's it! :)
Good day, friend.