SAT Math Multiple Choice Practice Question 518: Answer and Explanation

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Question: 518

17. ABCD is a quadrilateral such that AB = BC, AD = CD and AD = AB. If BC = 12, what is the perimeter of ABCD?

A. 44
B. 42
C. 40
D. 36
E. 33

Correct Answer: E


E Don't assume that the figure ABCD must be a rectangle; it doesn't have to be. All you need to do here is follow the rules: You know that AB = BC and that BC = 12, so you now know two of the four sides (sides AB and BC) are equal to 12. You know that AD is going to be one quarter of AB, so AD must be equal to 3. Finally, you know that AD is one half of CD, so CD must be equal to 6. This makes the total perimeter 12 + 12 + 3 + 6, or 33.

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