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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If triangle ABC above is congruent to triangle DEF (not shown), which of the following must be the length of one side of triangle DEF?

(A) 18
(B) 24
(C) 3 times (square root 6)
(D) 6 times (square root 3)
(E) It cannot be determined from the information given.

答案和解析

答案：D

解析：

Triangle ABC is congruent to triangle DEF, so the lengths of the three sides of triangle DEF are the same as the lengths of the three sides of triangle ABC. Triangle ABC is a 30 degrees - - 90 degrees triangle with hypotenuse of length 12, so the other two sides of triangle ABC have lengths 6 and 6 times (square root 3). Therefore, the lengths of the sides of triangle DEF must be 12, 6, and 6 times (square root 3). Of the choices given, only 6 times (square root 3) is one of these values.