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26 May 2017, 04:41
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Is \(a + b > c\)?
(1) \(a\), \(b\), and \(c\) represent three different lengths of the sides of a certain triangle
(2) \(a^{2} + b^{2} = c^{2}\)
(1) \(a\), \(b\), and \(c\) represent three different lengths of the sides of a certain triangle
(2) \(a^{2} + b^{2} = c^{2}\)
26 May 2017, 04:41
Kudos
Bookmarks
Official Solution:
According to the characteristics of a triangle, if you let \(a\), \(b\), and \(c\) represent the three different side lengths of a triangle, \(a - b < c < a + b\) appears often.
In other words, the sum of the lengths of the two sides is longer than the length of the other side. Therefore,
In the case of con 1), the condition is always yes, and sufficient
In the case of con 2), remember "CMT 3: con 1) and con 2) are mutually exclusive. Do not interfere with each other." It is not about the Pythagorean Theorem of a right triangle. If \((a, b, c) = (3, 4, 5)\), it is yes, but if \((a, b, c) = (-3, -4, 5)\), it is no, and not sufficient. Remember to consider the cases where there are negative integers.
Therefore, the answer is A. This is a question regarding "CMT 3: con 1) and con 2) are mutually exclusive. Do not interfere with each other. They are each an independent condition." When you look at con 2), you should not immediately relate to con 1).
Answer: A
According to the characteristics of a triangle, if you let \(a\), \(b\), and \(c\) represent the three different side lengths of a triangle, \(a - b < c < a + b\) appears often.
In other words, the sum of the lengths of the two sides is longer than the length of the other side. Therefore,
In the case of con 1), the condition is always yes, and sufficient
In the case of con 2), remember "CMT 3: con 1) and con 2) are mutually exclusive. Do not interfere with each other." It is not about the Pythagorean Theorem of a right triangle. If \((a, b, c) = (3, 4, 5)\), it is yes, but if \((a, b, c) = (-3, -4, 5)\), it is no, and not sufficient. Remember to consider the cases where there are negative integers.
Therefore, the answer is A. This is a question regarding "CMT 3: con 1) and con 2) are mutually exclusive. Do not interfere with each other. They are each an independent condition." When you look at con 2), you should not immediately relate to con 1).
Answer: A
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