Answer:
PR = 8
ST = 5
Please read the explanation below so next time you can do it yourself instead of resorting to an online answers forum. Enjoy~
Explanation:
In the left side triangle, I know that triangles PQS and PRS are congruent, so PQ and PR measures must be equivalent.
This is because of SAS (Side Angle Side) theorem. The marked congruent sides (QS and RS), the right angle, and the shared side PS make the triangles congruent.
Using CPCTC (Corresponding Parts of Congruent Triangles are Congruent), PQ and PR are congruent, and therefore PR is 8.
Moving on to triangle on the right side. The triangles VST and VUT are congruent by AAS theorem (Angle Angle Side).
Using CPCTC again, ST and UT are congruent. This makes the equation:
5z = 2z+3
Easy Algebra from here. -2z both sides, making:
3z = 3
Then divide:
z = 1
Plug in z and now you got:
ST and UT = 5
There you go! Not sure if you read this but eh. You're welcome :)