SAT Math Multiple Choice Practice Question 396: Answer and Explanation

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Question: 396


In the figure above, points C and D are midpoints of edges of a cube. A triangle is to be drawn with R and S as two of the vertices. Which of the following points should be the third vertex of the triangle if it is to have the largest possible perimeter?

A. A
B. B
C. C
D. D
E. E

Correct Answer: B


B Draw the five triangles. The simplest way to solve this problem is to compare the choices one pair at a time. For instance, it should be clear just by inspection that and , so we can eliminate A. Similarly, it should be clear that and , so we can eliminate C. Likewise, since RB > RD and SB > SD, we can eliminate D. Finally, we compare B with E. Since RB and RE are each a diagonal of one of the square faces, they must be equal. But SB is clearly longer than SE, because SB is the hypotenuse of triangle SEB, while SE is one of the legs.

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