GRE Math : How to find the perimeter of a rectangle

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 Perimeter Of A Rectangle

Quantity A

The perimeter of a square with a diagonal of 12 inches.

Quantity B

The perimeter of a rectangle with a diagonal of 10 inches and longer sides that are three times the length of its shorter sides.

Possible Answers:

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

The quantities are equal.

Correct answer:

Quantity A is greater.

Explanation:

The diagonal of a square creates a 45-45-90 triangle; therefore, considering x as the value for the sides of the square in A, set up the ratio: 1/√2 = x/12 → x = 12/√2

Simplify the square root out of the denominator: x = (12^√2)/2 = 6^√2. The perimeter is equal to 4x; therefore, quantity A is 24^√2.

Use the Pythagorean Theorem for B. We know that one side of the triangle is x and the other must be 3x. Furthermore, we know the hypotenuse is 10; therefore:

x²+ (3x)² = 10²→ x²+ 9x² = 100 → 10x² = 100 → x² = 10 → x = √10.

Transform the √10 into √2 * √5 ; therefore, x = √2 * √5 . The perimeter of the rectangle will equal 3x + 3x + x + x = 8x = 8√2 * √5 .

Compare these two values. Quantity A has a coefficient of 24 in for its √2 . Quantity B has a coefficient of 8√5, which must be smaller than 24, because 8 * 3 = 24, but √5 is less than 3 (which would be √9 ); therefore, A is larger.

Report an Error

Example Question #2 : How To Find The Perimeter Of A Rectangle

A rectangle has a length that is twice that of its height. If the perimeter of that rectangle is $20\:in$ , what is its area?

Possible Answers:

$400\:in^2$

$\frac{10}{3}\:in^2$

$\frac{200}{9}\:in^2$

$\frac{150}{7}\:in^2$

$\frac{250}{9}\:in^2$

Correct answer:

$\frac{200}{9}\:in^2$

Explanation:

Based on our first sentence, we know:

L=2H

The second sentence means:

$P=20\:in$ , which is the same as:

2L+2H=20

Now, we can replace with in the second equation:

2(2H)+2H=20

4H+2H=20

6H=20

3H=10

Therefore, $H=\frac{10}{3}\:in$

Now, this means that:

$L=2*\frac{10}{3}=\frac{20}{3}\:in$

If these are our values, then the area of the rectangle is:

$A=LH=\frac{10}{3}*\frac{20}{3}=\frac{200}{9}\:in^2$

Report an Error

Example Question #3 : How To Find The Perimeter Of A Rectangle

A rectangle with an area of 64 square units is one-fourth as wide as it is long. What is the perimeter of the rectangle?

Possible Answers:

Correct answer:

Explanation:

Begin by setting up a ratio of width to length for the rectangle. We know that the width is one-fourth the length, therefore

$\frac{1}{4}L=W$ .

Now, we can substitute W in the rectangle area formula with our new variable to solve for the length.

$A=W\cdot L$

$A=\left(\frac{1}{4}L\right)\cdot L$

$A=\frac{1}{4}L^2$

Solve for length:

$64=\frac{1}{4}L^2$

256=L^2

L=16

Using the length, solve for Width:

$W=\frac{1}{4}(16)$

W=4

Now, plug the length and width into the formula for the perimeter of a rectangle to solve:

P=2W+2L

P=2(4)+2(16)

P=8+32

P=40

The perimeter of the rectangle is 40.

Report an Error

All GRE Math Resources

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

Popular Subjects

French Tutors in Philadelphia, Algebra Tutors in Dallas Fort Worth, ISEE Tutors in Miami, ACT Tutors in Miami, MCAT Tutors in San Francisco-Bay Area, Reading Tutors in Seattle, GMAT Tutors in New York City, French Tutors in Miami, ISEE Tutors in Dallas Fort Worth, Physics Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in Miami, Spanish Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in New York City, LSAT Courses & Classes in San Diego, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Washington DC, GRE Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in Philadelphia, GRE Test Prep in Chicago, ACT Test Prep in Houston, ISEE Test Prep in Washington DC, SSAT Test Prep in Los Angeles, LSAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in Chicago, SAT Test Prep in Philadelphia, 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 perimeter of a rectangle

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #2 : How To Find The Perimeter Of A Rectangle

Example Question #3 : How To Find The Perimeter Of A Rectangle

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details