GRE Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for GRE Math

Create An Account Create Tests & Flashcards

All GRE Math Resources

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

Example Questions

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Daria and Ashley start at the same spot and walk their two dogs to the park, taking different routes. Daria walks 1 mile north and then 1 mile east. Ashley walks her dog on a path going northeast that leads directly to the park. How much further does Daria walk than Ashley?

Possible Answers:

√2 miles

1 mile

2+ √2 miles

Cannot be determined

2– √2 miles

Correct answer:

2– √2 miles

Explanation:

First let's calculate how far Daria walks. This is simply 1 mile north + 1 mile east = 2 miles. Now let's calculate how far Ashley walks. We can think of this problem using a right triangle. The two legs of the triangle are the 1 mile north and 1 mile east, and Ashley's distance is the diagonal. Using the Pythagorean Theorem we calculate the diagonal as √(1²+ 1²) = √2. So Daria walked 2 miles, and Ashley walked √2 miles. Therefore the difference is simply 2 – √2 miles.

Report an Error

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Which of the following sets of sides cannnot belong to a right triangle?

Possible Answers:

2, 2√3, 4

3, 4 ,5

2, 2, 2√2

6, 7, 8

5, 12, 13

Correct answer:

6, 7, 8

Explanation:

To answer this question without plugging all five answer choices in to the Pythagorean Theorem (which takes too long on the GRE), we can use special triangle formulas. Remember that 45-45-90 triangles have lengths of x, x, x√2. Similarly, 30-60-90 triangles have lengths x, x√3, 2x. We should also recall that 3,4,5 and 5,12,13 are special right triangles. Therefore the set of sides that doesn't fit any of these rules is 6, 7, 8.

Report an Error

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Max starts at PointAand travels 6 miles north to PointBand then 4 miles east to PointC. What is the shortest distance from PointAto PointC?

Possible Answers:

2√13 miles

5 miles

10 miles

4√2 miles

7 miles

Correct answer:

2√13 miles

Explanation:

This can be solved with the Pythagorean Theorem.

6²+ 4²=c²

52 =c²

c= √52 = 2√13

Report an Error

Example Question #51 :Triangles

Which set of side lengths CANNOT correspond to a right triangle?

Possible Answers:

6, 8, 11

5, 12, 13

3, 4, 5

8, 15, 17

7, 24, 25

Correct answer:

6, 8, 11

Explanation:

Because we are told this is a right triangle, we can use the Pythagorean Theorem,a²+b²=c². You may also remember some of these as special right triangles that are good to memorize, such as 3, 4, 5.

Here, 6, 8, 11 will not be the sides to a right triangle because 6²+ 8²= 10^2.

Report an Error

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel?

Possible Answers:

$\dpi{100} \small 12\ miles$

$\dpi{100} \small 16\ miles$

$\dpi{100} \small 10\ miles$

$\dpi{100} \small 8\ miles$

$\dpi{100} \small 14\ miles$

Correct answer:

$\dpi{100} \small 10\ miles$

Explanation:

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

$\dpi{100} \small 6^{2}+8^{2}=x^{2}$

$\dpi{100} \small 36+64=x^{2}$

$\dpi{100} \small x=10$ miles

Report an Error

Example Question #51 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Square PQRS is on the coordinate plane, and each side of the square is parallel to either the-axis or-axis. Pointhas coordinates $\left ( -2,-1 \right )$ and pointhas the coordinates $\left ( 3,4 \right )$ .

Quantity A: $5\sqrt{2}$

Quantity B: The distance between pointsand

Possible Answers:

Quantity B is greater.

The relationship cannot be determined from the information provided.

数量是gre考试ater.

The two quantities are equal.

Correct answer:

The two quantities are equal.

Explanation:

To find the distance between pointsand, split the square into two 45-45-90 triangles and find the hypotenuse. The side ratio of the 45-45-90 triangle is $s:s:s\sqrt{2}$ , so if the sides have a length of 5, the hypotenuse must be $5\sqrt{2}$ .

Report an Error

Example Question #341 :Triangles

Each of the following answer choices lists the side lengths of a different triangle. Which of these triangles does not have a right angle?

Possible Answers:

5, 12, 13

6,7,12

9, 12, 15

$2, 2, 2\sqrt{2}$

Correct answer:

6,7,12

Explanation:

6, 7, 12 cannot be the side lengths of a right triangle. 6^2+ 7^2 does not equal 12^2 . Also, special right triangle 3-4-5, 5-12-13, and 45-45-90 rules can eliminate all the other choices.

Report an Error

All GRE Math Resources

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

Popular Subjects

Calculus Tutors in Dallas Fort Worth,Reading Tutors in New York City,Physics Tutors in Boston,LSAT Tutors in San Diego,Reading Tutors in Atlanta,Physics Tutors in Atlanta,Spanish Tutors in Denver,English Tutors in Los Angeles,LSAT Tutors in Atlanta,MCAT Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Washington DC,Spanish Courses & Classes in Chicago,GRE Courses & Classes in Houston,ACT Courses & Classes in New York City,SSAT Courses & Classes in New York City,SAT Courses & Classes in Houston,MCAT Courses & Classes in Washington DC,MCAT Courses & Classes in Phoenix,ACT Courses & Classes in Denver,GRE Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Miami,ACT Test Prep in San Francisco-Bay Area,SAT Test Prep in Los Angeles,MCAT Test Prep in Boston,SSAT Test Prep in Seattle,GRE Test Prep in Phoenix,SAT Test Prep in San Francisco-Bay Area,ISEE Test Prep in Denver,MCAT Test Prep in Denver,GRE Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

请按照以下步骤文件通知:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

*Full legal name

Company name

*Phone number

*Email address

Address

*Address1

Address2

*City

*State

*Zipcode

*Country

Complaint Details

*URL of copyrighted work (where your original material is located)

*Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

*Signature (your digital signature is legally binding)

GRE Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #51 :Triangles

Example Question #1 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #51 :How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #341 :Triangles

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: