Explanation

In this question, we can see that the area of the lesser rectangle is 42, since it measures 6 by 7. We can draw a sketch:



We can see that the width of the larger rectangle is . Similarly, the other dimension will be , and the area of the larger rectangle will be:



This area minus the area of the smaller rectangle is 168, so



We can proceed by algebra or by answer-choice plugging. Let's try (B), :







This fits, so indeed the correct answer is (B).

This question is well-suited for answer-plugging; not only are the answer choice numbers friendly to work with, but if an answer is not correct, it's clear whether we will need a bigger or smaller number, to make the bigger rectangle bigger or smaller. Nevertheless, the plugging goes most swiftly if our understanding is set up with the diagram and the equation. Again, the correct answer is (B).