We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the length of the side of a rhombus

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 Next →

Example Question #221 : Intermediate Geometry

Given that a rhombus has a perimeter of 90in , find the length of a side of the rhombus.

Possible Answers:

30.5in

30in

22.5in

16in

Correct answer:

22.5in

Explanation:

To find the length of one side of the rhombus, apply the formula:

P=4S , where is the side length.

Since we are given the perimeter, we plug that value into the equation and solve for .

90=4(S)
$S=\frac{90}{4}=22.5$

Report an Error

Example Question #62 : Rhombuses

Given that a rhombus has an area of square units, and a height of . What is the length of one side of the rhombus?

Possible Answers:

12.5

Correct answer:

Explanation:

To find the length of a side of the rhombus, work backwards using the area formula:

$Area=(base\times height)$

Since we are given the area and the height, we plug these values into the equation and solve for the base.

$70=(base\times height)$

$70=(base\times 5)$

$base=\frac{70}{5}=14$

Report an Error

Example Question #63 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$\sqrt2$

$\sqrt6$

Cannot be determined

$\sqrt5$

Correct answer:

$\sqrt5$

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{2}{2}=1$

$\frac{\text{Diagonal 2}}{2}=\frac{4}{2}=2$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$1^2+2^2=\text{side length}^2$

$\text{side length}^2=1+4=5$

$\text{side length}=\sqrt5$

Report an Error

Example Question #64 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$\sqrt{29}$

$\sqrt{35}$

$3\sqrt3$

$\sqrt{31}$

Correct answer:

$\sqrt{29}$

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{4}{2}=2$

$\frac{\text{Diagonal 2}}{2}=\frac{10}{2}=5$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$2^2+5^2=\text{side length}^2$

$\text{side length}^2=4+25=29$

$\text{side length}=\sqrt{29}$

Report an Error

Example Question #65 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$6\sqrt{10}$

$12\sqrt2$

$2\sqrt{34}$

$3\sqrt{15}$

Correct answer:

$2\sqrt{34}$

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{12}{2}=6$

$\frac{\text{Diagonal 2}}{2}=\frac{20}{2}=10$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$6^2+10^2=\text{side length}^2$

$\text{side length}^2=36+100=136$

$\text{side length}=2\sqrt{34}$

Report an Error

Example Question #66 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$19\sqrt{3}$

$\sqrt{170}$

$2\sqrt{77}$

Correct answer:

$\sqrt{170}$

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{14}{2}=7$

$\frac{\text{Diagonal 2}}{2}=\frac{22}{2}=11$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$7^2+11^2=\text{side length}^2$

$\text{side length}^2=49+121=170$

$\text{side length}=\sqrt{170}$

Report an Error

Example Question #67 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$\sqrt{145}$

$3\sqrt{15}$

$7\sqrt3$

$12\sqrt2$

Correct answer:

$\sqrt{145}$

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{16}{2}=8$

$\frac{\text{Diagonal 2}}{2}=\frac{18}{2}=9$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$8^2+9^2=\text{side length}^2$

$\text{side length}^2=64+81=145$

$\text{side length}=\sqrt{145}$

Report an Error

Example Question #68 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$5\sqrt3$

$2\sqrt3$

Correct answer:

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{6}{2}=3$

$\frac{\text{Diagonal 2}}{2}=\frac{8}{2}=4$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$3^2+4^2=\text{side length}^2$

$\text{side length}^2=9+16=25$

$\text{side length}=5$

Report an Error

Example Question #69 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$3\sqrt3$

$\sqrt{26}$

$\sqrt{39}$

Correct answer:

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{10}{2}=5$

$\frac{\text{Diagonal 2}}{2}=\frac{24}{2}=12$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$5^2+12^2=\text{side length}^2$

$\text{side length}^2=25+144=169$

$\text{side length}=13$

Report an Error

Example Question #70 : Rhombuses

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Possible Answers:

$8\sqrt3$

$11\sqrt2$

Correct answer:

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{12}=\frac{2}{2}=6$

$\frac{\text{Diagonal 2}}{2}=\frac{16}{2}=8$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$6^2+8^2=\text{side length}^2$

$\text{side length}^2=36+64=100$

$\text{side length}=10$

Report an Error

← Previous 1 2 3 4 5 Next →

View Tutors

Ahmad
Certified Tutor

American University of Beirut, Bachelor of Science, Chemistry. Wayne State University, Doctor of Philosophy, Organic Chemistry.

View Tutors

Traci
Certified Tutor

California State University-Fullerton, Bachelor of Science, History. UNLV, Masters in Education, Early Childhood Education.

View Tutors

Natasha
Certified Tutor

Tufts University, Bachelor in Arts, Asian Studies. New York University, Master of Arts Teaching, Teaching English as a Second...

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Phoenix, GRE Tutors in Boston, GMAT Tutors in Seattle, SSAT Tutors in Dallas Fort Worth, Computer Science Tutors in Atlanta, Spanish Tutors in Houston, Algebra Tutors in San Francisco-Bay Area, Calculus Tutors in Los Angeles, Chemistry Tutors in Miami, SAT Tutors in Dallas Fort Worth

Popular Courses & Classes

ISEE Courses & Classes in Atlanta, ISEE Courses & Classes in Denver, SSAT Courses & Classes in San Diego, SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, Spanish Courses & Classes in Los Angeles

Popular Test Prep

GMAT Test Prep in New York City, SSAT Test Prep in Philadelphia, MCAT Test Prep in Washington DC, ACT Test Prep in Miami, SAT Test Prep in Miami, GRE Test Prep in New York City, SAT Test Prep in Seattle, MCAT Test Prep in Phoenix, SSAT Test Prep in Miami, SSAT Test Prep in Dallas Fort Worth

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : How to find the length of the side of a rhombus

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #221 : Intermediate Geometry

Example Question #62 : Rhombuses

Example Question #63 : Rhombuses

Example Question #64 : Rhombuses

Example Question #65 : Rhombuses

Example Question #66 : Rhombuses

Example Question #67 : Rhombuses

Example Question #68 : Rhombuses

Example Question #69 : Rhombuses

Example Question #70 : Rhombuses

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: