SAT Math Multiple Choice Practice Question 28: Answer and Explanation

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Question: 28

6. A square is changed into a rectangle by adding 3 meters to one side and subtracting 2 meters from the other side. The new rectangle has an area of 50 square meters. Find the original length of a side of the square.

A. 5 meters
B. 6 meters
C. 7 meters
D. 8 meters
E. 9 meters

Correct Answer: C


C. As is often the case on the SAT, the trial-and-error method works great here. If you don't want to use trial and error, you can call the original side of the square x, making the rectangle's sides x + 3 and x - 2. Because the area is 50, you write (x + 3)(x - 2) = 50. Use the FOIL method to get x2 - 2x + 3x - 6 = 50, or x2 + x - 56 = 0. (Remember, to solve a quadratic equation, you must make one side equal zero.) You can factor this equation into (x + 8)(x - 7) = 0. This equation is true when x equals either -8 or 7, but it doesn't make sense for a square to have a side of -8. Therefore, 7 is your answer. (Turn to Chapter 14 for more info on the FOIL method.)

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