GRE Math : Acute / Obtuse Triangles

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Example Questions

Example Question #4 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Triangle

A:12

B:3

C:14

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

Possible Answers:

$\textup{A, B, and C.}$

$\textup{A and B.}$

$\textup{A only.}$

$\textup{C only.}$

$\textup{B only.}$

Correct answer:

$\textup{A and B.}$

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:

|a-b|<c<a+b

For the triangle given:

|6-8|<c<6+8

2<c<14 .

Both choices A and B satisfy this criteria.

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Example Question #3 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

A triangle has sides of lengths and

Quantity A: The length of the missing side.

Quantity B:

Possible Answers:

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

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.

|a-b|<c<|a+b|

|7-13|<c<|7+13|

6<c<20

The missing side must be greater than .

Quantity A is greater.

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Example Question #82 : Geometry

The lengths of two sides of a triangle are and .

Quantity A: The length of the missing side.

Quantity B:

Possible Answers:

Quantity B is greater.

The relationship cannot be determined.

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 3-4-5 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:

|3-4|<c<3+4

1<c<7

There are plenty of potential lengths that fall above and below . The relationship cannot be determined.

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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.

The two quantities are equal.

Quantity A is greater.

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.

|a-b|<c<|a+b|

|5-16|<c<|5+16|

11<c<21

For a triangle with sides and , there is no way a side could be .

Quantity B is greater.

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All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

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GRE Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #4 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #82 : Geometry

Example Question #81 : Geometry

All GRE Math Resources

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