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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 A B C above is congruent to triangle D E F (not shown), which of the following must be the length of one side of triangle D E F?

(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 A B C is congruent to triangle D E F, so the lengths of the three sides of triangle D E F are the same as the lengths of the three sides of triangle A B C. Triangle A B C is a 30 degrees - - 90 degrees triangle with hypotenuse of length 12, so the other two sides of triangle A B C have lengths 6 and 6 times (square root 3). Therefore, the lengths of the sides of triangle D E F 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.