下面是一道关于几何方面的SAT数学题的解答方法详细分析，来自SAT考试的官方网站collegeboard。这是一类关于分析可能性的SAT数学题，这种题在SAT数学考试当中经常会见到，考察大家考虑问题是否全面的能力。下面是详细内容。

　　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.

　　以上就是这道SAT数学题的详细解答方法的全部内容，对这道SAT数学题中的每一个可能的答案都进行了分析。大家在备考的时候可以按照上面所列的方法进行，这样在考试的时候就可以更加快速而且有效率的解答相关的SAT数学题目了。

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