Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #20 : Isosceles Triangles

Isosceles

In an isosceles right triangle, two sides equal $\displaystyle x$. Find the length of side $\displaystyle h$.

Possible Answers:

$\sqrt{2}$ $\displaystyle \sqrt{2}$

$2\sqrt{2}$ $\displaystyle 2\sqrt{2}$

$\sqrt{x}$ $\displaystyle \sqrt{x}$

$\displaystyle x$

$x\sqrt{2}$ $\displaystyle x\sqrt{2}$

Correct answer:

$x\sqrt{2}$ $\displaystyle x\sqrt{2}$

Explanation:

This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal $\displaystyle x$, $\displaystyle x$, and $x\sqrt{2}$ $\displaystyle x\sqrt{2}$. However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem $(a^{2}+b^{2}=c^{2})$ $\displaystyle (a^{2}+b^{2}=c^{2})$.

$h^{2}=x^{2}+x^{2}$ $\displaystyle h^{2}=x^{2}+x^{2}$

$h^{2}=2x^{2}$ $\displaystyle h^{2}=2x^{2}$

$h=\sqrt{2x^{2}}$ $\displaystyle h=\sqrt{2x^{2}}$

$\rightarrow x\sqrt{2}$ $\displaystyle \rightarrow x\sqrt{2}$

Report an Error

Example Question #1 : 45/45/90 Right Isosceles Triangles

ABCD is a square whose side is $\displaystyle 8$ units. Find the length of diagonal AC.

Possible Answers:

$\displaystyle 16$

$8\sqrt{3}$ $\displaystyle 8\sqrt{3}$

$\displaystyle 12$

none of the other answers

$8 \sqrt{2}$ $\displaystyle 8 \sqrt{2}$

Correct answer:

$8 \sqrt{2}$ $\displaystyle 8 \sqrt{2}$

Explanation:

To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of $\displaystyle 45$, $\displaystyle 45$, and $\displaystyle 90$ degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the $\displaystyle 45$ degree angles serving as x, and the side opposite the $\displaystyle 90$ degree angle serving as $x\sqrt{2}$ $\displaystyle x\sqrt{2}$.

Appyling this, if we plug $\displaystyle 8$ in for $\displaystyle x$ we get that the side opposite the right angle (aka the diagonal) is $8\sqrt{2}$ $\displaystyle 8\sqrt{2}$

Report an Error

Example Question #2 : 45/45/90 Right Isosceles Triangles

The area of a square is 144 $\displaystyle 144$. Find the length of the diagonal of the square.

Possible Answers:

$\displaystyle 12$

$4\sqrt{2}$ $\displaystyle 4\sqrt{2}$

$16\sqrt{2}$ $\displaystyle 16\sqrt{2}$

$\displaystyle 16$

$12\sqrt{2}$ $\displaystyle 12\sqrt{2}$

Correct answer:

$12\sqrt{2}$ $\displaystyle 12\sqrt{2}$

Explanation:

If the area of the square is 144 $\displaystyle 144$, we know that each side of the square is $\displaystyle 12$, because the area of a square is $s^{2}$ $\displaystyle s^{2}$.

Then, the diagonal creates two $\displaystyle 45/45/90$special right triangles. Knowing that the sides = $\displaystyle 12$, we can find that the hypotenuse (aka diagonal) is $12\sqrt{2}$ $\displaystyle 12\sqrt{2}$

Report an Error

View Tutors

Jecintha
Certified Tutor

Metropolitan College of New York, Bachelor in Arts, Human Services.

View Tutors

Latoshia
Certified Tutor

ITT Technical Institute-Nashville, Bachelor of Science, Management Information Systems. Colorado Technical University-Colorad...

View Tutors

LeVette
Certified Tutor

Liberty University, Bachelor of Science, Business Administration and Management. Liberty University, Master of Arts, Organiza...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in San Francisco-Bay Area, Calculus Tutors in Phoenix, French Tutors in Washington DC, Reading Tutors in San Francisco-Bay Area, GRE Tutors in Phoenix, GMAT Tutors in Houston, Computer Science Tutors in Seattle, Calculus Tutors in Houston, ACT Tutors in Denver, LSAT Tutors in New York City

Popular Courses & Classes

GRE Courses & Classes in Houston, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Boston, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Miami, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Houston, ACT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Washington DC, SAT Test Prep in Los Angeles, ACT Test Prep in Chicago, SAT Test Prep in Houston, GRE Test Prep in Denver, LSAT Test Prep in Miami, ISEE Test Prep in Chicago, ISEE Test Prep in Washington DC, GRE Test Prep in Boston, ACT Test Prep in Washington DC

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

High School Math : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #20 : Isosceles Triangles

Example Question #1 : 45/45/90 Right Isosceles Triangles

Example Question #2 : 45/45/90 Right Isosceles Triangles

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: