Final answer:
To find the length of bar PQ, we can use the concept of similar polygons and set up a proportion using the corresponding sides of the quadrilaterals ABCD and PQRS. The length of bar PQ can be found by solving the proportion and isolating x.
Step-by-step explanation:
In order to find the length of bar PQ, we can use the concept of similar polygons. Since quadrilaterals ABCD and PQRS are similar, their corresponding sides are proportional.
Let's denote the length of bar AB as y. Since AC = 3R and AB = 3x, we can set up the following proportion: AC/AB = R/x. Substitute the given values, AC = 3R and AB = 3x, and solve for x.
3R/3x = R/x. Simplify the equation and cross multiply: 3Rx = 3Rx. Divide both sides by 3R to isolate x: x = R.