Answer: 2.8 inches
Explanation:
Given : The beams intersect each other to form two similar triangles ΔQRP and ΔARC .
PR = 3.4 inches
CR = 5.1 inches.
AC = 4.2 inches
To find : PQ
We know that the corresponding sides of two similar triangles are proportional.
i.e. for similar triangles ΔQRP and ΔARC , we have

Hence, the distance between the endpoints of the beams P and Q = 2.8 inches
.