Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Right Triangles

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 #97 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the length of the hypotenuse of a right triangle whose other sides are 5cm and 12cm?

Possible Answers:

18cm

4.24cm

7cm

60cm

13cm

Correct answer:

13cm

Explanation:

Use Pythagorean Theorem

a^2+b^2=c^2

a and b are the sides of the triangle

(5)^2+(12)^2=c^2

c^2=169

c=13

Report an Error

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Prblem 6 basic geometry

Find the length of the hypotenuse in triangle ABC

Possible Answers:

$\sqrt{400}inches$

$\sqrt{256}inches$

$15\ inches$

$91\ inches$

$\sqrt{365}inches$

Correct answer:

$\sqrt{365}inches$

Explanation:

To find the length of the hypotenuse, use the Pythagorean Theorem.

a^2+b^2=c^2

a=14 inches

b=13 inches

c=???

14^2+13^2=c^2

196 + 169 = 365

365=c^2

Now take the square root of both sides.

$\sqrt{365}=c$

Report an Error

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Three sides of a right triangle are A,B, and C. Side C is the hypotenuse.

A=3 . B=4 . Find .

Possible Answers:

C=4

C=25

C=7

C=5

Correct answer:

C=5

Explanation:

To solve for the value of c, you would use the Pythagorean theorem, which states

A^2+B^2=C^2 .

Plugging in the values we have, we get

3^2+4^2=C^2 .

To solve for c, we take the square root of both sides.

$\sqrt{3^2+4^2}=\sqrt {C^2}$ .

$\sqrt{25}=5=C$ .

Report an Error

Example Question #103 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse, , of a triangle whose other sides are A=9 and B=40 .

Possible Answers:

C=40

C=42

C=41

C=20

Correct answer:

C=41

Explanation:

To find the length of the hypotenuse, we must use the Pythagorean Theorem,

A^2+B^2=C^2 .

Using the values given,

$9^2+41^2=C^2\rightarrowC=\sqrt{81+1681}=42$ .

Report an Error

Example Question #141 : Right Triangles

Find the length of the hypotenuse of a triangle with legs 3 and 7.

Possible Answers:

$\sqrt{52}$

$\sqrt{58}$

$\sqrt{40}$

Correct answer:

$\sqrt{58}$

Explanation:

Use Pythagorean Theorem: 3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

$\sqrt{58 } = c$

Report an Error

Example Question #104 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Shape area right triangle

In the right triangle shown here, a=8 and b=15 . What is the length of the remaining side?

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean Theorem, the relationship between a right triangle's height , its base , and its hypotenuse is given by

a^2+b^2=c^2 .

Here, a=8 and b=15 . The length of the remaining side can be calculated as follows:

a^2+b^2=c^2

8^2+15^2=c^2

64+225=c^2

289=c^2

$\Rightarrow c= \sqrt{289}=17$ .

Hence, the length of this right triangle's hypotenuse is units.

Report an Error

Example Question #1322 : Basic Geometry

If one leg of a right triangle is 6in and the other leg is 8in, what is the measure of the hypotenuse?

Possible Answers:

$12\text{ in}$

$10\text{ in}$

$14\text{ in}$

$9\text{ in}$

$11\text{ in}$

Correct answer:

$10\text{ in}$

Explanation:

First we need to know Pythagorean Theorem states that what when we take the square of one leg and add it to the square of the other leg, we get the hypotenuse squared or $a^{2}+b^{2}=c^{2}$ where a and b represent the short legs and c represents the hypotenuse (long side of the triangle opposite the right angle).

Since the short legs of our triangles are 6 and 8 we can set up our equation as follows:

$6^{2}+8^{2}=c^{2}$

Now we solve

36 + 64 =100

Since $c^{2}=100$ we take the square root of both sides and we get c=10 .

So the hypotenuse measures 10 inches.

Report an Error

Example Question #161 : Geometry

Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?

Possible Answers:

200

100

Correct answer:

100

Explanation:

Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.

At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.

You can save time by using the 3:4:5 common triangle. 60 and 80 are $3\cdot 20$ and $4\cdot 20$ , respectively, making the hypotenuse equal to $5\cdot 20=100$ .

We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Substitute the following known values into the formula and solve for the missing hypotenuse: side .

$a= 60,\ b= 80,\ c= ?$

$(60)^{2}+(80)^{2}=c^{2}$

$3600+6400=c^{2}$

$10,000=c^{2}$

c=100

Susie will walk 100 meters to reach her house.

Report an Error

Example Question #441 : Plane Geometry

The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?

Possible Answers:

Correct answer:

Explanation:

First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as , the next side will be defined as x+2 , and the longest side will be defined as x+4 . We can then find the perimeter of a triangle using the following formula:

$\text{Perimeter}=\text{side}+\text{side}+\text{side}$

Substitute in the known values and variables.

$\text{Perimeter}=x+(x+2)+(x+4)$

57=3x+6

Subtract 6 from both sides of the equation.

57-6=3x+6-6

51=3x

Divide both sides of the equation by 3.

$\frac{51}{3}=\frac{3x}{3}$

Solve.

x=17

This is not the answer; we need to find the length of the longest side, or x+4 .

$\text{Longest side}=x+4$

Substitute in the calculated value for and solve.

$\text{Longest side}=17+4$

$\text{Longest side}=21$

The longest side of the triangle is 21 centimeters long.

Report an Error

Example Question #5 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Each of the following answer choices lists the side lengths of a different triangle. Which of these triangles does not have a right angle?

Possible Answers:

9, 12, 15

$2, 2, 2\sqrt{2}$

5, 12, 13

6,7,12

Correct answer:

6,7,12

Explanation:

6, 7, 12 cannot be the side lengths of a right triangle. 6^2+ 7^2 does not equal 12^2 . Also, special right triangle 3-4-5, 5-12-13, and 45-45-90 rules can eliminate all the other choices.

Report an Error

View Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

View Tutors

Lucinda
Certified Tutor

South University-Savannah, Bachelor of Science, Health Services Administration.

View Tutors

Fitsum
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Biological and Physical Sciences.

All Basic Geometry Resources

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

Popular Subjects

ISEE Tutors in Washington DC, SSAT Tutors in Denver, Statistics Tutors in Atlanta, Biology Tutors in Seattle, Physics Tutors in Houston, Chemistry Tutors in San Francisco-Bay Area, ISEE Tutors in Boston, Computer Science Tutors in San Francisco-Bay Area, Calculus Tutors in Atlanta, Algebra Tutors in Philadelphia

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, MCAT Courses & Classes in Miami, SSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in New York City, GRE Courses & Classes in Boston, ISEE Courses & Classes in New York City

Popular Test Prep

GRE Test Prep in Miami, ISEE Test Prep in Miami, LSAT Test Prep in Chicago, MCAT Test Prep in New York City, MCAT Test Prep in Seattle, SAT Test Prep in Washington DC, MCAT Test Prep in Boston, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Boston, LSAT 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 : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #97 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #103 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #141 : Right Triangles

Example Question #104 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1322 : Basic Geometry

Example Question #161 : Geometry

Example Question #441 : Plane Geometry

Example Question #5 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: