Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Plane Geometry

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 #2 : How To Find The Length Of The Diagonal Of A Square

Find the length of the square's diagonal.

Square_8

Possible Answers:

$8\sqrt2$

$4\sqrt5$

None of the other answers are correct.

Correct answer:

$8\sqrt2$

Explanation:

The diagonal line cuts the square into two equal triangles. Their hypotenuse is the diagonal of the square, so we can solve for the hypotenuse.

We need to use the Pythagorean Theorem: c^2=a^2+b^2 , where a and b are the legs and c is the hypotenuse.

The two legs have lengths of 8. Plug this in and solve for c:

c^2=8^2+8^2=64+64=128

$c=\sqrt{128}=\sqrt{2\cdot 64}=8\sqrt2$

Report an Error

Example Question #5 : How To Find The Length Of The Diagonal Of A Square

Find the length of the diagonal of a square that has side lengths of cm.

Possible Answers:

$25\text{ cm}$

$16\text{ cm}$

$10\text{ cm}$

$4\text{ cm}$

$4\sqrt{2}$ $\text{cm}$

Correct answer:

$4\sqrt{2}$ $\text{cm}$

Explanation:

You can do this problem in two different ways that lead to the final answer:

1. Pythagorean Theorem

2. Special Triangles (45-45-90)

1. For the first idea, use the Pythagorean Theorem: a^2 +b^2 =c^2 , where a and b are the side lengths of the square and c is the length of the diagonal.

4^2+4^2=c^2

c^2=32

$c=\sqrt{32}$

$c=\sqrt{16*2}=\sqrt{16}\, \times \sqrt{2} = 4\sqrt{2}$

2. If you know that ALL squares can be made into two special right triangles such that their angles are 45-45-90, then there's a formula you could use:

Let's say that your side length of the square is "a". Then the diagonal of the square (or the hypotenuse of the right triangle) will be $a\sqrt{2}$ .

So using this with a=4:

$4\sqrt{2}$

Report an Error

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

The perimeter of a square is 48. What is the length of its diagonal?

Possible Answers:

$12\sqrt{2}$

$2\sqrt{12}$

$24\sqrt{2}$

$\sqrt{12}$

$48\sqrt{2}$

Correct answer:

$12\sqrt{2}$

Explanation:

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

side^2 + side^2 = hypotenuse^2

12^2+12^2=hypotenuse^2

144 + 144=hypotenuse^2

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Report an Error

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

The perimeter of a square is units. How many units long is the diagonal of the square?

Possible Answers:

$7\sqrt2$

$14\sqrt3$

$14\sqrt2$

Correct answer:

$7\sqrt2$

Explanation:

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

4s=28

s=7

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

a^2+b^2=c^2

7^2+7^2=c^2

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

Report an Error

Example Question #2 : Squares

Find the length of the diagonal of the square with a side length of .

Possible Answers:

$8\sqrt2$

$4\sqrt2$

4.5

Correct answer:

$4\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=4\sqrt2$

Report an Error

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$20\sqrt2$

$10\sqrt2$

$5\sqrt2$

$2\sqrt2$

Correct answer:

$10\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=10\sqrt2$

Report an Error

Example Question #5 : Squares

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$15\sqrt2$

$30\sqrt2$

$7\sqrt2$

Correct answer:

$15\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=15\sqrt2$

Report an Error

Example Question #661 : Plane Geometry

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$6\sqrt2$

$3\sqrt2$

$9\sqrt2$

Correct answer:

$3\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=3\sqrt2$

Report an Error

Example Question #261 : Quadrilaterals

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$11\sqrt2$

$16\sqrt2$

$22\sqrt2$

$15\sqrt2$

Correct answer:

$22\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=22\sqrt2$

Report an Error

Example Question #262 : Quadrilaterals

Find the length of the diagonal of a square with a side length of .

Possible Answers:

$6\sqrt2$

$16\sqrt2$

$12\sqrt2$

Correct answer:

$12\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=12\sqrt2$

Report an Error

View Tutors

Michele
Certified Tutor

University of Rome, Professional (JD, MD, DMD, etc), Law. Saint John's University -NY, Master of Science, Marketing.

View Tutors

Angela
Certified Tutor

Kent State University at Kent, Bachelor of Science, Middle School Teaching.

View Tutors

Richard
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Chemistry. CUNY Brooklyn College, Master of Arts, Experimental Psychology.

All Basic Geometry Resources

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

Popular Subjects

Calculus Tutors in Phoenix, Computer Science Tutors in Dallas Fort Worth, ACT Tutors in Denver, SAT Tutors in Los Angeles, ISEE Tutors in Atlanta, ACT Tutors in Chicago, LSAT Tutors in San Francisco-Bay Area, English Tutors in San Francisco-Bay Area, SAT Tutors in Boston, MCAT Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Washington DC, GMAT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Houston, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Atlanta, Spanish Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in Chicago, GMAT Test Prep in Seattle, GRE Test Prep in Los Angeles, SAT Test Prep in San Diego, SAT Test Prep in Washington DC, ACT Test Prep in Miami, LSAT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, ACT 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

Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #2 : How To Find The Length Of The Diagonal Of A Square

Example Question #5 : How To Find The Length Of The Diagonal Of A Square

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

Example Question #2 : Squares

Example Question #3 : How To Find The Length Of The Diagonal Of A Square

Example Question #5 : Squares

Example Question #661 : Plane Geometry

Example Question #261 : Quadrilaterals

Example Question #262 : Quadrilaterals

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: