SAT Math Multiple Choice Practice Question 132: Answer and Explanation

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Question: 132


The diagram above shows two rectangles, ABCD and PQRS. If AP = 4, QR = 7, and RD = , then the area of PQRS is

A. 84
C. 147
D. 231

Correct Answer: C


C. Because you know QR, your goal is to find either RS or PQ. Now, PS must be the same as QR, so PS = 7 and the Pythagorean Theorem tells you that . The next key step is to realize that triangles APS and DSR are similar, because angles A and D are both right angles, while APS and DSP are also congruent. Thus, triangle DSR is exactly three times as big as triangle APS, so SR is just three times bigger than PS, and SR = 21. Finally, the area of PQRS is 7 × 21 = 147.

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