# SAT Math Multiple Choice Practice Question 396: Answer and Explanation

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**Question: 396**

**22.**

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

**Explanation:**

**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.