Final answer:
The length x of side PQ in the similar quadrilaterals can be found by setting up a proportion. After cross-multiplying, x is found to be 1.125 which is not in the given options, suggesting there may be a misprint in the question or options.
Step-by-step explanation:
The student's question asks about finding the length x of side PQ in similar quadrilaterals ABCD and PQRS. In similar figures, corresponding sides are proportional, and the ratios of their lengths are the same. Since you provided that side AD in the larger quadrilateral is 4 units and the corresponding side RS in the smaller one is 1.5 units, you can set up a proportion to solve for the length x of side PQ, which corresponds to side BC in the larger quadrilateral.
Let x be the length of side PQ (which corresponds to side BC in the larger quadrilateral) and 3 units be the length of side BC. We then have the proportion:
AD/RS = BC/PQ
4/1.5 = 3/x
By cross-multiplying and solving for x, we get:
4x = 3 * 1.5
4x = 4.5
x = 4.5 / 4
x = 1.125
However, since 1.125 is not one of the provided options, it appears there may be a misprint in the question or the given options. The closest number to 1.125 is option (c) which is 1.5. If you could provide the correct measurements or options, I would be able to give you a more accurate answer.