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SAT数学典型题解析

2019-10-15 21:52:18来源:网络

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  If two sides of the triangle above have lengths and , the perimeter of the triangle could be which of the following?

  Answer Choices

  (A) only

  (B) only

  (C) only

  (D) and only

  (E) , , and

  The correct answer is B

  Explanation

  Difficulty: Hard

  In questions of this type, statements , , and should each be considered independently of the others. You must determine which of those statements could be true.

  Statement cannot be true. The perimeter of the triangle cannot be , since the sum of the two given sides is without even considering the third side of the triangle.

  Continuing to work the problem, you see that in , if the perimeter were , then the third side of the triangle would be , or . A triangle can have side lengths of , , and . So the perimeter of the triangle could be .

  Finally, consider whether it is possible for the triangle to have a perimeter of . In this case, the third side of the triangle would be . The third side of this triangle cannot be , since the sum of the other two sides is not greater than . By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the correct answer is only.

  以上就是关于“SAT数学典型题解析”的内容,更多精彩内容,请关注SAT频道!


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