GRE Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for GRE Math

Create An Account

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 Side Of A Right Triangle

2 triangles are similar

Triangle 1 has sides 6, 8, 10

Triangle 2 has sides 5 , 3, x

find x

Possible Answers:

Correct answer:

Explanation:

Draw the triangles

Triangle 1 is a 6,8,10 right triangle with 10 as the hypotenuse

Triangle 2: 3 is half of 6, 5 is half of 10; x must be half of 8

Report an Error

Example Question #1 : Right Triangles

Given the diagram, indicate if Quantity A is larger, Quantity B is larger, if they are equal, or if there is not enough information given to determine the relationship.

Quantity A: $\dpi{100} \small x$

Quantity B: 7.5

Possible Answers:

The relaionship cannot be determined from the information given.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

Since this is a 30-60-90 triangle, we know that the length of the side opposite the 60 degree angle is $\dpi{100} \small \sqrt{3}$ times the side opposite the 30 degree angle. Thus, $\dpi{100} \small 5\sqrt{3}$ , which is about 8.66. This is larger than 7.5.

Report an Error

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

A right triangle's perimeter is $\dpi{100} \small 3+\sqrt{3}$ . The other two angles of the triangle are 30 degrees and 60 degrees.

Quantity A: The triangle's hypotenuse length

Quantity B: 2

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

Correct answer:

The two quantities are equal.

Explanation:

The ratio of the sides of a 30-60-90 triangle is $\dpi{100} \small x:x{\sqrt{3}}:2x$ , with the hypotenuse being $\dpi{100} \small 2x$ . Thus, the perimeter of this triangle would be $\dpi{100} \small x+x\sqrt{3}+2x=3x\sqrt{3}$ . Since the triangle depicted in this problem has a perimeter of $\dpi{100} \small 3\sqrt{3}$ , $\dpi{100} \small x$ must equal 1, which would make the hypotenuse equal to 2.

Report an Error

Example Question #101 : Geometry

If the shortest side of a right triangle has length x-4 and its hypotenuse has length x+4 , what is the length of the remaining side?

Possible Answers:

4x^2

$4\sqrt{x}$

Correct answer:

$4\sqrt{x}$

Explanation:

Use the Pythagorean theorem, $a^2 + b^2 = c^2$ , with $\dpi{100} \small a=x-4$ and $\dpi{100} \small c=x+4$ , and solve for $\dpi{100} \small b$ .

$(x-4)^2 + b^2 = (x+4)^2$

Rearrange to isolate $\dpi{100} \small b^{2}$ :

$b^2 = (x+4)^2 - (x-4)^2$

$b^2 = (x+4)(x+4) - (x-4)(x-4)$

Use FOIL to multiply out:

$b^2 = (x^2 + 8x + 16) - (x^2 - 8x + 16)$

Distribute the minus sign to rewrite without parentheses:

$b^2 = x^2 + 8x + 16 - x^2 + 8x - 16$

Combine like terms:

$b^2 = 16x$

Take the square root of both sides:

$b = 4\sqrt{x}$

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Given the following triangle, what is the length of the unknown side?

Gre triangle

Possible Answers:

The answer cannot be determined from the information given.

$\sqrt{313}$

Correct answer:

The answer cannot be determined from the information given.

Explanation:

At first sight, it's tempting to assume this is a right triangle and to thus use the Pythagorean Theorem to find a length of 5 for the missing side.

However, the triangle was not stated to be a right triangle in the problem statement, and no indication was given in the drawing to indicate that it was a right triangle either, such as a square demarcation in the vertex opposite the side measuring 13.

Thus there is not enough information to give the length of the missing side. When taking standardized math tests, be careful making assumptions about information that is not given.

Report an Error

All GRE Math Resources

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

Popular Subjects

English Tutors in Dallas Fort Worth, French Tutors in Los Angeles, Statistics Tutors in New York City, MCAT Tutors in Washington DC, SSAT Tutors in San Diego, Calculus Tutors in Houston, LSAT Tutors in Los Angeles, Calculus Tutors in San Diego, Reading Tutors in Chicago, Statistics Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Boston, Spanish Courses & Classes in Houston, SSAT Courses & Classes in Denver, SSAT Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Denver, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in New York City, ACT Test Prep in Chicago, LSAT Test Prep in San Diego, SSAT Test Prep in Houston, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Seattle, GMAT Test Prep in Denver, MCAT Test Prep in Atlanta, GRE Test Prep in Denver, ACT Test Prep in Miami

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.

Please follow these steps to file a notice:

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)

Email address:
Your name:
Feedback:

GRE Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : Right Triangles

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Example Question #101 : Geometry

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details