Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #24 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$\sqrt{34}$

$\sqrt{33}$

$\sqrt{35}$

Correct answer:

$\sqrt{34}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{3^2 + 5^2}=\sqrt{34}$

Report an Error

Example Question #292 : Triangles

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$\sqrt{66}$

$\sqrt{65}$

$\sqrt{69}$

Correct answer:

$\sqrt{65}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{7^2 + 4^2}=\sqrt{65}$

Report an Error

Example Question #1281 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$3\sqrt3$

$\sqrt{15}$

$\sqrt{14}$

$4\sqrt2$

Correct answer:

$\sqrt{14}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(2\sqrt2)^2$

Simplify.

c^2=6+8

Solve.

c^2=14

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{14}$

Report an Error

Example Question #1281 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$6\sqrt2$

$\sqrt{26}$

$4\sqrt5$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(\sqrt{19})^2$

Simplify.

c^2=6+19

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

Example Question #293 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt3$

$2\sqrt6$

$5\sqrt2$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{11})^2+(\sqrt{14})^2$

Simplify.

c^2=11+14

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

Example Question #301 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt2$

$\sqrt{26}$

$3\sqrt3$

Correct answer:

$\sqrt{26}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{10})^2+(4)^2$

Simplify.

c^2=10+16

Solve.

c^2=26

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{26}$

Report an Error

Example Question #302 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$6\sqrt5$

$8\sqrt3$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{10})^2+(\sqrt{39})^2$

Simplify.

c^2=10+39

Solve.

c^2=49

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{49}$

Simplify.

c=7

Report an Error

Example Question #303 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt6$

The length of the hypotenuse cannot be determined.

$16\sqrt2$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(2\sqrt{5})^2+(\sqrt{29})^2$

Simplify.

c^2=20+29

Solve.

c^2=49

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{49}$

Simplify.

c=7

Report an Error

Example Question #304 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt{14}$

$14\sqrt2$

$2\sqrt{14}$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{2})^2+(\sqrt{14})^2$

Simplify.

c^2=2+14

Solve.

c^2=16

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{16}$

Simplify.

c=4

Report an Error

Example Question #305 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{39}$

$3\sqrt{13}$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{3})^2+(\sqrt{13})^2$

Simplify.

c^2=3+13

Solve.

c^2=16

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{16}$

Simplify.

c=4

Report an Error

View Tutors

Nicholas
Certified Tutor

Stony Brook University, Bachelor of Science, Mechanical Engineering.

View Tutors

Pranathi
Certified Tutor

PES University, Bachelor of Science, Biomedical Engineering. Duke University, Master of Science, Bioethics and Medical Ethics.

View Tutors

Krystal
Certified Tutor

University of Central Florida, Doctor of Education, Curriculum and Instruction.

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Atlanta, Computer Science Tutors in Miami, Physics Tutors in Los Angeles, English Tutors in Seattle, GMAT Tutors in Atlanta, MCAT Tutors in Seattle, GMAT Tutors in Miami, Chemistry Tutors in Miami, LSAT Tutors in Washington DC, GMAT Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston, Spanish Courses & Classes in Miami, ISEE Courses & Classes in Atlanta, MCAT Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Chicago, ISEE Test Prep in Los Angeles, SSAT Test Prep in Phoenix, SAT Test Prep in Boston, ISEE Test Prep in Miami, ISEE Test Prep in Chicago, MCAT Test Prep in Houston, MCAT Test Prep in Boston, ISEE Test Prep in Atlanta, ISEE Test Prep in San Francisco-Bay Area

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

Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #24 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #292 : Triangles

Example Question #1281 : Basic Geometry

Example Question #1281 : Basic Geometry

Example Question #293 : Triangles

Example Question #301 : Triangles

Example Question #302 : Triangles

Example Question #303 : Triangles

Example Question #304 : Triangles

Example Question #305 : Triangles

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: