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a,b, and c represent the side lengths of a certain triangle
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04 Mar 2021, 02:35
04 Mar 2021, 02:35
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a,b, and c represent the side lengths of a certain triangle
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
2a + 3b |
2b+c |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
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Posts: 6218
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a,b, and c represent the side lengths of a certain triangle
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04 Mar 2021, 07:24
04 Mar 2021, 07:24
1
Carcass wrote:
a,b, and c represent the side lengths of a certain triangle
Quantity A |
Quantity B |
2a + 3b |
2b + c |
Let's first simplify the question using matching operations (my favorite Quantitative Comparison strategy)
Given:
Quantity A: 2a + 3b
Quantity B: 2b + c
Subtract 2b from both quantities to get:
Quantity A: 2a + b
Quantity B: c
Key property: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
Since c is the length of the third side, we can apply the property to write: a - b < c < a + b
If c < a + b, it must also be true that c < a + b + a (since a > 0)
In other words, it must be true that c < 2a + b
Answer: A
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Affiliations: Prepster Education
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Re: a,b, and c represent the side lengths of a certain triangle
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04 Mar 2021, 07:41
04 Mar 2021, 07:41
1
Carcass wrote:
a,b, and c represent the side lengths of a certain triangle
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
2a + 3b |
2b+c |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
We know, any side in a triangle is less than the sum of other 2 sides and greater than the positive difference between other 2.
Here, \(|a - b| < c < a + b\)
Col. A: \(2a + 3b\)
Col. B: \(2b + c\)
Subtract \(2b\) from both sides;
Col. A: \(2a + b\)
Col. B: \(c\)
Since \(c < a + b\), it must also be less than \(2a + b\)
Hence, option A
