GRE Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #81 : Geometry

Triangle

What is a possible value for the length of the missing side?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #81 : Geometry

A triangle has sides of lengths  and 

Quantity A: The length of the missing side.

Quantity B: 

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

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.

 

Example Question #83 : Geometry

The lengths of two sides of a triangle are  and .

Quantity A: The length of the missing side.

Quantity B: 

Possible Answers:

The relationship cannot be determined.

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

Correct answer:

The relationship cannot be determined.

Explanation:

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.

Example Question #81 : Geometry

A triangle has sides  and 

Quantity A: The length of the missing side.

Quantity B: 

Possible Answers:

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

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.

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