We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 Next →

Example Question #121 : Plane Geometry

Find the length of the hypotenuse.

Triangle_4_14_c

Note: This is a right triangle.

Possible Answers:

$\sqrt{91}$

$4\sqrt{53}$

$2\sqrt{53}$

Correct answer:

$2\sqrt{53}$

Explanation:

To find the length of this 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.

Here, c is our missing hypotenuse length, a = 4 ,and b = 14.

Plug these values in and solve for c:

c^2=4^2+14^2=16+196=212

$c=\sqrt{212}=\sqrt{4 \cdot 53}=\sqrt{4}\sqrt{53}=2\sqrt{53}$

Report an Error

Example Question #61 : Triangles

Side in the triangle below (not to scale) is equal to . Side is equal to . What is the length of side ?

Right_triangle_with_labeled_sides

Possible Answers:

$\ 146$

$\sqrt{146}$

$\sqrt{135}$

Correct answer:

$\sqrt{146}$

Explanation:

Use the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$ , where a and b are the legs and c is the hypotenuse.

We know and , so we can plug them in to solve for c:

$5^{2}+11^{2}=c^{2}$

$25+121=c^{2}$

$146=c^{2}$

$c=\sqrt{146}$

Report an Error

Example Question #61 : Right Triangles

Dan drives 5 miles north and then 8 miles west to get to school. If he walks, he can take a direct path from his house to the school, cutting down the distance. How long is the path from Dan's house to his school?

Possible Answers:

9.43 miles

4.36 miles

19 miles

13 miles

89 miles

Correct answer:

9.43 miles

Explanation:

We are really looking for the hypotenuse of a triangle that has legs of 5 miles and 8 miles.

Apply the Pythagorean Theorem:

a² + b² = c²

25 + 64 = c²

89 = c²

c = 9.43 miles

Report an Error

Example Question #41 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with side lengths and ?

Possible Answers:

Correct answer:

Explanation:

The Pythagorean Theorem states that . This question gives us the values of and , and asks us to solve for .

Take and and plug them into the equation as and :

$12^{2}+16^{2}=c^{2}$

Now we can start solving for :

$144+256=c^{2}$

$400=c^{2}$

$\sqrt{400}=\sqrt{c^{2}}$

20=c

The length of the hypotenuse is .

Report an Error

Example Question #45 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

One leg of a triangle measures 12 inches. Which of the following could be the length of the other leg if the hypotenuse is an integer length?

Possible Answers:

$4\ inches$

$16\ inches$

$20\ inches$

$15\ inches$

$12\ inches$

Correct answer:

$16\ inches$

Explanation:

By the Pythagorean Theorem, if is the hypotenuse and and are the legs, $c = \sqrt{a^{2}+b^{2}}}$ .

Set a=12 , the known leg, and rewrite the above as:

$c = \sqrt{12^{2}+b^{2}}}$

$c = \sqrt{144+b^{2}}}$

We can now substitute each of the five choices for ; the one which yields a whole number for is the correct answer choice.

b=4 :

$c = \sqrt{144+4^{2}}} = \sqrt{144+16}} =\sqrt{160}=12.64...$

b=12 :

$c = \sqrt{144+12^{2}}} = \sqrt{144+144}} =\sqrt{288}=16.97...$

b=15 :

$c = \sqrt{144+15^{2}}} = \sqrt{144+225}} =\sqrt{369}=19.20...$

b=16 :

$c = \sqrt{144+16^{2}}} = \sqrt{144+256}} =\sqrt{400}=20$

b=20 :

$c = \sqrt{144+20^{2}}} = \sqrt{144+400}} =\sqrt{544}=23.32...$

The only value of which yields a whole number for the hypotenuse is 16, so this is the one we choose.

Report an Error

Example Question #62 : Triangles

Find the perimeter of the polygon.

Possible Answers:

Correct answer:

Explanation:

Divide the shape into a rectangle and a right triangle as indicated below.

Find the hypotenuse of the right triangle with the Pythagorean Theorem, a^2 + b^2 = c^2 , where and are the legs of the triangle and is its hypotenuse.

(8)^2+(6)^2 = c^2

100 = c^2

$\sqrt{100} = \sqrt{c^2}$

c =10

This is our missing length.

Now add the sides of the polygon together to find the perimeter:

20 + 10 + 26 + 8 = 64

Report an Error

Example Question #61 : Triangles

The lengths of the sides of a right triangle are consecutive integers, and the length of the shortest side is . Which of the following expressions could be used to solve for ?

Possible Answers:

(x)(x+1)=(x+2)^2

(x+2)-(x+1)=x

x^2+(x+1)^2=(x+2)^2

x^2+(x+2)^2=(x+4)^2

x+x-3=x

Correct answer:

x^2+(x+1)^2=(x+2)^2

Explanation:

Since the lengths of the sides are consecutive integers and the shortest side is , the three sides are , (x+1) , and (x+2) .

We then use the Pythagorean Theorem:

$\newline a^2+b^2=c^2 \newline x^2+(x+1)^2=(x+2)^2$

Report an Error

Example Question #81 : Triangles

Square PQRS is on the coordinate plane, and each side of the square is parallel to either the -axis or -axis. Point has coordinates $\left ( -2,-1 \right )$ and point has the coordinates $\left ( 3,4 \right )$ .

Quantity A: $5\sqrt{2}$

Quantity B: The distance between points and

Possible Answers:

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information provided.

Correct answer:

The two quantities are equal.

Explanation:

To find the distance between points and , split the square into two 45-45-90 triangles and find the hypotenuse. The side ratio of the 45-45-90 triangle is $s:s:s\sqrt{2}$ , so if the sides have a length of 5, the hypotenuse must be $5\sqrt{2}$ .

Report an Error

Example Question #91 : Plane Geometry

Two sides of a given triangle are both . If one angle of the triangle is a right angle, then what is the measure of the hypotenuse?

Possible Answers:

$7\sqrt{5}$

$5\sqrt{2}$

$2\sqrt{5}$

Correct answer:

$5\sqrt{2}$

Explanation:

If we know two sides are equal to and we know that one of the angles is a right angle, then that means that this must be a Special Right Triangle where the interior angles are $90$^{\circ}$, 45$^{\circ}$, 45$^{\circ}$$ .

With this special triangle, we also know that the measure of the hypotenuse is equal to the measure of one side of the triangle times the square root of that measure.

Since one leg of the triangle is . then the hypotenuse is equal to $5\sqrt{2}$ .

We could also solve this using the Pythagorean Theorem, like so:

$c^2=\sqrt{5^2+5^2}=\sqrt{50}=\sqrt{2\cdot25}=5\sqrt{2}$

Report an Error

Example Question #13 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$30\textup{ ft}$

$45\textup{ ft}$

$25\textup{ ft}$

$35\textup{ ft}$

$22\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

Report an Error

← Previous 1 2 3 4 5 6 Next →

View SAT Mathematics Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View SAT Mathematics Tutors

Stanley
Certified Tutor

Trinity University, Bachelor of Science, Engineering Science.

View SAT Mathematics Tutors

Aashish
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Biological and Physical Sciences. University of Toledo, Doctor of M...

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Miami, Spanish Courses & Classes in San Diego, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Miami, ISEE Courses & Classes in New York City, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Atlanta, GRE Test Prep in Miami, SAT Test Prep in Los Angeles, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Phoenix, ACT Test Prep in Miami, SSAT Test Prep in Phoenix, ACT Test Prep in Los Angeles, MCAT Test Prep in Philadelphia

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

SAT Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #121 : Plane Geometry

Example Question #61 : Triangles

Example Question #61 : Right Triangles

Example Question #41 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #45 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #62 : Triangles

Example Question #61 : Triangles

Example Question #81 : Triangles

Example Question #91 : Plane Geometry

Example Question #13 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: