How to find the length of the side of an acute / obtuse triangle - GRE Quantitative Reasoning
Card 1 of 64
Which of these side lengths cannot form a triangle?
Which of these side lengths cannot form a triangle?
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Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
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The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
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If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
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Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Tap to reveal answer
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
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What is a possible value for the length of the missing side?
What is a possible value for the length of the missing side?
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For a triangle where the length of two sides, 
and 
, is the only information known, the third side, 
, is limited in the following matter:
For the triangle given:
.
Both choices A and B satisfy this criteria.
For a triangle where the length of two sides,
For the triangle given:
Both choices A and B satisfy this criteria.
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A triangle has sides of lengths 
and 
Quantity A: The length of the missing side.
Quantity B: 
A triangle has sides of lengths
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than 
.
Quantity A is greater.
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than
Quantity A is greater.
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A triangle has sides 
and 
Quantity A: The length of the missing side.
Quantity B: 
A triangle has sides
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides 
and 
, there is no way a side could be 
.
Quantity B is greater.
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides
Quantity B is greater.
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The lengths of two sides of a triangle are 
and 
.
Quantity A: The length of the missing side.
Quantity B: 
The lengths of two sides of a triangle are
Quantity A: The length of the missing side.
Quantity B:
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Seeing the sides 
and 
may bring to mind a 
triangle. However, we've been told nothing about the angles of the triangle. It could be right, or it could be obtuse or acute.
Since the angles are unknown, the side is bounded as follows:
There are plenty of potential lengths that fall above and below 
. The relationship cannot be determined.
Seeing the sides
Since the angles are unknown, the side is bounded as follows:
There are plenty of potential lengths that fall above and below
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Which of these side lengths cannot form a triangle?
Which of these side lengths cannot form a triangle?
Tap to reveal answer
Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
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The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
Tap to reveal answer
If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
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Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Tap to reveal answer
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
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What is a possible value for the length of the missing side?
What is a possible value for the length of the missing side?
Tap to reveal answer
For a triangle where the length of two sides, and , is the only information known, the third side, , is limited in the following matter:
For the triangle given:
.
Both choices A and B satisfy this criteria.
For a triangle where the length of two sides,
For the triangle given:
Both choices A and B satisfy this criteria.
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A triangle has sides of lengths and
Quantity A: The length of the missing side.
Quantity B:
A triangle has sides of lengths
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than .
Quantity A is greater.
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than
Quantity A is greater.
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A triangle has sides and
Quantity A: The length of the missing side.
Quantity B:
A triangle has sides
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides and , there is no way a side could be .
Quantity B is greater.
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides
Quantity B is greater.
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The lengths of two sides of a triangle are and .
Quantity A: The length of the missing side.
Quantity B:
The lengths of two sides of a triangle are
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
Seeing the sides and may bring to mind a triangle. However, we've been told nothing about the angles of the triangle. It could be right, or it could be obtuse or acute.
Since the angles are unknown, the side is bounded as follows:
There are plenty of potential lengths that fall above and below . The relationship cannot be determined.
Seeing the sides
Since the angles are unknown, the side is bounded as follows:
There are plenty of potential lengths that fall above and below
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Which of these side lengths cannot form a triangle?
Which of these side lengths cannot form a triangle?
Tap to reveal answer
Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
Two sides of a triangle must add up to greater than the third side. 25, 37, 66 cannot be the lengths of the sides of a triangle as 25 + 37 < 66.
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The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
The sides of a triangle are 6, 12, and an integer x. How many possible values does x have?
Tap to reveal answer
If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
If two sides of a triangle are 6 and 12, the third must be greater than 12-6 and less than 12+6 since two sides cannot be summed to be greater than the third side in a triangle. There are 11 possible values for x: 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17.
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Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Two sides of a triangle are 5 and 7. Which CANNOT be the length of the third side?
Tap to reveal answer
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
12: The sum of two sides of a triangle must be greater than the third side. Therefore, the length of the third side would have to be less than 12 and greater than 2.
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What is a possible value for the length of the missing side?
What is a possible value for the length of the missing side?
Tap to reveal answer
For a triangle where the length of two sides, and , is the only information known, the third side, , is limited in the following matter:
For the triangle given:
.
Both choices A and B satisfy this criteria.
For a triangle where the length of two sides,
For the triangle given:
Both choices A and B satisfy this criteria.
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A triangle has sides of lengths and
Quantity A: The length of the missing side.
Quantity B:
A triangle has sides of lengths
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than .
Quantity A is greater.
If two sides of a triangle are known and all angles are unknown, the length of the third side is limited by the difference and sum of the other two sides.
The missing side must be greater than
Quantity A is greater.
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A triangle has sides and
Quantity A: The length of the missing side.
Quantity B:
A triangle has sides
Quantity A: The length of the missing side.
Quantity B:
Tap to reveal answer
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides and , there is no way a side could be .
Quantity B is greater.
If two sides of a triangle are known and the angles of the triangle are unknown, the length of the missing side is limited by the difference and sum of the other two sides.
For a triangle with sides
Quantity B is greater.
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