On this problem, the key is to change the diagram according to the information that the problem gives you, or to see that Q is like a "half-way point" where both sides have to meet on your line.
We are given that BC is equal to 4. So write 4 on that side.
Additionally, we know that P and Q are "symmetric" about line AB, so that means they have equal length on both sides of line AB. So what you do now is you draw those old fashion congruency marks (the small verticle dashes). Since they are equal, give them each a number less than 4, since Q is inside the rectangle ABCD, whose width is 4. So give them each a length of 2, or any other number < 4.
Can you guess what the next step is?
They also tell you Q and R are symmetric about line CD. So put two congruency marks on both sides of CD. Now give them each a length that is 4 minus the number you gave the first two equal parts. If you picked 2, you would now also pick 2 (4-2 = 2).
Now you have 4 congruent parts: each length 2. The total width is 8, answer choice B.
Now you might be saying to yourself: How do I know the rectangle is bisected? You don't. But the answer holds true regardless what numbers you picked the symmetric parts to be. For example, if the first two parts had been 3.5 each, and the other two .5 each,
PR would have still come out to a total length of 8. (3.5*2 + .5*2=8)
The most important insight to make here is to realize that you can create a line according to what the problem is giving you. When the SAT gives you a diagram, they want to confuse with it, but at the same time they want you to use what's given either in the text or the diagram to solve the problem. Since the diagram is not drawn to scale, they want you to use the text to solve the problem. The diagram is really only useful for you to make the connecton that both sides of QR and PQ meet to make a line. Knowing that, the text's directions allow you to solve the problem.
Andre
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