Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : How to find the height of a 45/45/90 right isosceles triangle

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 #51 : 45/45/90 Right Isosceles Triangles

$\fn_cm In\;\Delta ABC,\;\angle BAC=45^{\circ }.$

$\angle BCA = \, ?$

Possible Answers:

$\fn_cm 45^{\circ}$

$135^{\circ}$

$60^{\circ}$

$90^{\circ}$

Correct answer:

$\fn_cm 45^{\circ}$

Explanation:

$The\;degrees\;in\;a\;triangle\;sum\;to\;180^{\circ}. \; 180^{\circ}-90^{\circ}-45^{\circ}=45^{\circ}.$

Report an Error

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Find the height of the 45-45-90 right triangle with a hypotenuse of $15\sqrt{6}$ .

Possible Answers:

$15\sqrt{3}$

$15\sqrt{2}$

7.5

$\sqrt{6}$

Correct answer:

$15\sqrt{3}$

Explanation:

If the hypotenuse of a 45-45-90 right triangle is $15\sqrt{6}$ then:

The height and the base of the triangle will be the same length since it is a 45-45-90 triangle (isosceles).

a^2+b^2=c^2

Since both a and b will be equal let's use a=b=x and $c=15\sqrt{6}$ :

$x^2 +x^2=(15\sqrt{6})^2$

2x^2=225*6

2x^2=1350

x^2=675

$x=\sqrt{675}$

$x=\sqrt{225*3}$

$x=\sqrt{225}\, \sqrt{3}$

$x=15\sqrt{3}$

Report an Error

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

What is the height of a 45/45/90 triangle if its hypotenuse is $2\sqrt7$ cm.

Find_the_height

Possible Answers:

2cm

28cm

14 cm

3cm

$\sqrt{14} cm$

Correct answer:

$\sqrt{14} cm$

Explanation:

Given that is a 45/45/90 triangle, it means that it's also isosceles. Because the hypotenuse if 2√7 cm, that means that the base and the height (the two remaining sides) will be equivalent.

The length of one of the legs can be solved for in one of two ways.

1. The Pythagorean Theorem

2. Using Find_the_leg_length_resolution

Using the Pythagorean Theorem, a^2+b^2=c^2 , we've already determined that "a" and "b" are the same number. Lets say a=b=s . This allows for the equation to be rewritten as s^2+s^2=c^2 , which may be simplified into ${\color{Purple} 2s^2=c^2}$

Because s is our unknown, we will be solving for s.

$2s^2=(2\sqrt{7})^2$

$2s^2=4\sqrt{49}$

2s^2=28

$s^2=\frac{28}{2}$

s^2=14

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

${\color{Blue} s=\sqrt{14} cm}$

Report an Error

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height?

Possible Answers:

$\frac{13}{2}$

$\frac{15\sqrt2}{2}$

$\frac{13\sqrt2}{2}$

Correct answer:

$\frac{13\sqrt2}{2}$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{13\sqrt2}{2}$

Report an Error

Example Question #2 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height of the triangle?

Possible Answers:

$\frac{21\sqrt2}{2}$

$21\sqrt3$

Correct answer:

$\frac{21\sqrt2}{2}$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{21\sqrt2}{2}$

Report an Error

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is 212 , what is the length of the height?

Possible Answers:

$212\sqrt2$

$181\sqrt2$

$106\sqrt2$

$126\sqrt2$

Correct answer:

$106\sqrt2$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{212\sqrt2}{2}$

Simplify.

$\text{height}=106\sqrt2$

Report an Error

Example Question #3 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height of the triangle?

Possible Answers:

$6\sqrt2$

$12\sqrt2$

Correct answer:

$6\sqrt2$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{12\sqrt2}{2}$

Simplify.

$\text{height}=6\sqrt2$

Report an Error

Example Question #7 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height?

Possible Answers:

$40\sqrt2$

$24\sqrt3$

$14\sqrt2$

$28\sqrt2$

Correct answer:

$28\sqrt2$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{56\sqrt2}{2}$

Simplify.

$\text{height}=28\sqrt2$

Report an Error

Example Question #4 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height?

Possible Answers:

$33\sqrt2$

$66\sqrt2$

$55\sqrt2$

$44\sqrt2$

Correct answer:

$33\sqrt2$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{66\sqrt2}{2}$

Simplify.

$\text{height}=33\sqrt2$

Report an Error

Example Question #2 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

If the hypotenuse of an isoceles right triangle is , what is the length of the height?

Possible Answers:

$68\sqrt2$

$34\sqrt2$

$14\sqrt3$

$60\sqrt3$

Correct answer:

$34\sqrt2$

Explanation:

An isoceles right triangle is another way of saying that the triangle is a 45-45-90 triangle.

Now, recall the Pythagorean theorem:

$\text{base}^2+\text{height}^2=\text{hypotenuse}^2$

Because we are working with a 45-45-90 triangle, the base and the height have the same length. We can rewrite the above equation as the following:

$\text{height}^2+\text{height}^2=\text{hypotenuse}^2$

$2(\text{height})^2=\text{hypotenuse}^2$

$\text{height}^2=\frac{\text{hypotenuse}^2}{2}$

$\text{height}=\sqrt{\frac{\text{hypotenuse}^2}{2}}$

Simplify.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}$

Multiply the fraction by one in the form of:

$1\rightarrow \frac{\sqrt{2}}{\sqrt{2}}$

Substitute.

$\text{height}=\frac{\text{hypotenuse}}{\sqrt2}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{height}=\frac{\text{hypotenuse}(\sqrt2)}{2}{}$

Now, substitute in the value of the hypotenuse to find the height for the given triangle.

$\text{height}=\frac{68\sqrt2}{2}$

Simplify.

$\text{height}=34\sqrt2$

Report an Error

View Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Tutors

Alyce
Certified Tutor

The University of Alabama, Master of Arts, German.

All Basic Geometry Resources

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

Popular Subjects

French Tutors in Los Angeles, Chemistry Tutors in Chicago, English Tutors in Miami, ISEE Tutors in Miami, MCAT Tutors in San Francisco-Bay Area, LSAT Tutors in New York City, ACT Tutors in Philadelphia, Calculus Tutors in Atlanta, Math Tutors in Seattle, Algebra Tutors in San Diego

Popular Courses & Classes

ISEE Courses & Classes in Chicago, LSAT Courses & Classes in Miami, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in New York City, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Los Angeles, MCAT Test Prep in Los Angeles, GRE Test Prep in Boston, ACT Test Prep in New York City, GRE Test Prep in Phoenix, ISEE Test Prep in Miami, LSAT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Atlanta, GMAT Test Prep in New York City

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 height of a 45/45/90 right isosceles triangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #51 : 45/45/90 Right Isosceles Triangles

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #2 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #1 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #3 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #7 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #4 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

Example Question #2 : How To Find The Height Of A 45/45/90 Right Isosceles Triangle

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: